how to calculate the first hundred terms of a sequence​

Answers

Answer 1

Answer:

Question: what is the sum of the first 100 whole numbers?? how am i supposed to work this out efficiently? thanks

The question you asked relates back to a famous mathematician, Gauss. In elementary school in the late 1700’s, Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher, but Gauss found the answer rather quickly by discovering a pattern. His observation was as follows:

1 + 2 + 3 + 4 + … + 98 + 99 + 100

Gauss noticed that if he was to split the numbers into two groups (1 to 50 and 51 to 100), he could add them together vertically to get a sum of 101.

1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

.

.

.

48 + 53 = 101

49 + 52 = 101

50 + 51 = 101

Gauss realized then that his final total would be 50(101) = 5050.

The sequence of numbers (1, 2, 3, … , 100) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:

S is the sum of the series and n is the number of terms in the series, in this case, 100.

Hope this helps!


Related Questions

Vascular Tissue is mostly likely to be found in the___of a plant’s shoot
- Center
- Between the center and outside
- None of these
- Outside

Answers

Vascular tissue is mostly likely to be found in the outside

plants are able to bend their stem so they are closer to a light source________
what adaption do they use?
structural
physiological
behavioral

Answers

Answer:

I think its physiological (B)

Explanation:

In phototropism a plant bends or grows directionally in response to light. Shoots usually move towards the light; roots usually move away from it.

Plants have a variety of developmental, physiological, and growth responses to light—sometimes only to particular wavelengths of light.

(Credits to Khan academy) Hope im right and hope it helps.

How are mitosis and meiosis similar?

A.
both require DNA replication

B.
both have two cell divisions

C.
both produce gametes

D.
both involve crossing over

Answers

I think is d,,,,,,,,,,,,,,,,

Helppp I need to put this question in my own words!!!

Answers

Answer:

A planet revolves around the sun while the moon orbits a planet

7. Show that it we cross pure grech pea plants with the heterozygous yellow pea plants
what are the possible phenistkes of the first filial generation by using rennut square
I use crosses the first filial generation on the question number seven (7) what are the
possible ration of their offspring's
9. What are the most commah known neuroplerans nictter are​

Answers

Explanation:

7. 100% green pea plant

-50%=GG

-50%=Gg

9. Not sure what you mean?

Answer:

Yellow( heterozygous) and green

Explanation:

Q4: Describe how crossing over can lead to new variations in genes. ​

Answers

Answer:

Crossing-over is the exchange of genetic material between homologous chromosomes. It results in new combinations of genes on each chromosome. When cells divide during meiosis, homologous chromosomes are randomly distributed to daughter cells, and different chromosomes segregate independently of each other.

Explanation:

please give me brainlist and follow

A marathon runner is running a race. During the race the marathon runners heart rate and breathing increases. Which of the following explains why the marathon runners' body is responding in this way?

Answers

Answer:

Warmer temperatures increase your heart rate. In addition to pumping more blood to the muscles, your heart also transports more blood to the skin in order to cool it. Increased demand causes your heart to beat faster -- anywhere from 20 to 40 beats per minute higher than normal.

Explanation:

Hope this helped. =)

Answer for 10 points please

Answers

all the letters that are the same. LL, hh, aa, TT, GG,OO,EE,vv,dd,yy,zz,AA

The _________________________ are responsible for packaging and distributing the materials in a cell. * Fill in the blank(s) with the correct answer.

Answers

Red blood cells I think!

What characteristic could provide a species with a better chance of surviving a drastic environmental change?

(A) A small population size

(B) A highly diversified gene pool

(C) specialized cells within the body

(D) Many individuals with the recessive trait

Answers

the answer is B


Species with a limited variety of phenotypes and where all members of the species are similar to one another have a smaller chance of coping with environmental variability compared to a species with greater diversity.

A highly diversified gene pool could provide a species with a better chance of surviving a drastic environmental change. So, the correct option is B.

What is Diversified Gene pool?

Greater genetic diversity within a population is made possible by a diverse gene pool, which raises the possibility that at least some members of the population will exhibit features that are more adapted to the new environment.

This variety can develop as a result of gene flow from other populations or mutations. The number of people having the recessive trait or a limited population size, however, would not always give an advantage in enduring environmental change. A species may have a better chance of surviving a severe environmental shift if its gene pool is extremely varied.

Therefore, the correct option is B.

Learn more about Gene pool, here:

https://brainly.com/question/1027582

#SPJ2

For Ascomycota, what structure's function is most similar to the function of a mushroom?
a
Ascus.

b
Ascocarp.

c
Antheridium.

d
Archegonium.

e
Ascospore.

Answers

Answer:

e. Ascospore

hope this helps

what best describes a steppe

Answers

Answer:

a wide expanse of desert. a grassland with few trees.

Explanation:

please I need help on it​

Answers

Answer:

c) Symbiosis.........

What does a DNA repair mutation cause in the Cell cycle?

Answers

Answer:

Mutation rates increase substantially in cells defective in DNA mismatch repair or in homologous recombinational repair (HRR). Chromosomal rearrangements and aneuploidy also increase in HRR defective cells. Higher levels of DNA damage not only cause increased mutation, but also cause increased epimutation.

To measure gas in a car by unit what would you measure by? Cup?Pint?Quart?or gallon.

Answers

Gallons. You buy gasoline by the gallon.

Answer:

Gallon

Explanation:

help pleaseee

give an example of lamarcks theory of evolution:

Answers

Lamarck believed that elephants all used to have short trunks. When there was no food or water that they could reach with their short trunks, they stretched their trunks to reach the water and branches, and their offspring inherited long trunks.

Which are examples of pathogens? (Choose all that apply)
Parasite
Virus
Plants
Water
Fungi
Bacteria
Poop

Answers

Answer:

virus

bacteria

fungi

poop

Explanation:

I’ll mark u as brainliest!

Answers

The cell looks identical on both sides of the second picture. This shows that the cell is getting ready to split into two separate cells.

how do Solids, liquids and gasses change states?

Answers

you melt a solid to turn into a liquid, then you boil the liquid to turn it into gas

Someone already answered but i’m going to provide more detail.
If you have an ice cube which is a solid and it melts, it turns into liquid water instead of frozen. Now, if you put that same water in a pot on top of a stovetop, once it reaches boiling point (212°F) then it will turn into a gas and start to bubble. I hope this helps! :]

Which tree above shows a different evolutionary history from the others? Explain your answer.[ ]

Answers

Answer:

the second one is the right answer

The second evolutionary tree (2) is showing a different evolutionary history from the other trees.

What is an evolutionary tree?

An evolutionary tree is a diagram/graphic used in biology to show evolutionary relationships between taxa.

The taxa located at the tree can be different species, genera, orders, etc.

An evolutionary tree is monophyletic when all descendants originated from the same ancestor.

In conclusion, the second evolutionary tree is showing a different evolutionary history from the other trees.

Learn more in:

https://brainly.com/question/2189834

Explain the importance of organic compounds to the cell.

Answers

Answer:

Organic compounds essential to human functioning include carbohydrates, lipids, proteins, and nucleotides. ... Monomers are single units of organic compounds. They bond by dehydration synthesis to form polymers, which can in turn be broken by hydrolysis. Carbohydrate compounds provide essential body fuel.

pls help on the question below

Answers

it would be #3, a turtle digging a hole to lay eggs
answer:
#3

step by step:

which one is the lowest ,middle and highest between these magnification
10X
30X
40X​

Answers

Answer:

10X is lowest

30X is middle

40X is highest

who is in charge in canada

Answers

Answer:

Justin Trudeau

Explanation:

Deputy Prime Minister of Canada

Avanti works in a bookstore. She has four books and is going to place them in two stacks. The diagram above shows the books before they touch. Use the information in the diagram to answer the question. How did the temperatures of the four books compare before they touched? How will the temperatures of the two top books compare after the books have been touching for a while, and why? HELP

Answers

Answer:

Well they didn't transfer any energy when they weren’t touching and it didn't produce any energy if it didn’t move. Since they are on top of each other they are causing momentum on each other creating kinetic energy

Explanation:

help guysssss with my 73 points as plssssss​

Answers

Answer:

I'm pretty sure it's oil gland hope this helps

the answer is d) oil gland


What process leads to the specialization of the embryonic stem cells into different types of cells?
O differentiation
division
O replication
O respiration

Answers

the answer is differentiation

Why is it important to center the object you want to look at in your field of view before changing to a higher magnification objective lens? A. So the object is still in your field of view at the higher magnification. B. So you can always see the entire object at the higher magnification. C. So you do not damage the higher magnification objective lens.​

Answers

Answer:

B. So you can always see the entire object at the higher magnification

Explanation:

A microscope is used to view objects smaller than the naked or unaided eyes can see. The objective lens, in conjunction with the occular or eye lens, is used to achieve this purpose. The objective lens are of different magnifications as follows: 10X, 40X, 100X etc.

However, as the magnification increases i.e. higher objective, the object in the field of view becomes smaller and less focused. Hence, the object in the field of view must first be centered at a lower magnification/objective lens before changing to a higher one in order for the entire object to be seen at a higher magnification.

Labrador retrievers are traditionally black, brown, or yellow. The B allele codes for black fur, and the b allele codes for brown fur. The E allele allows the pigment to be deposited in the fur, while the e allele doesn't allow the pigment to be deposited. If one lab has the genotype bbee, and another lab has the genotype BbEe, what is the chance that an offspring will be brown

Answers

Answer:

25% of offspring will be brown

Explanation:

4 out of 16 of will be brown

to convert this to a percentage do:

4 ÷ 16 × 100 = 25

Punnett squares are in the image

Brown offspring are circled

Oxygen-rich blood is carried through pulmonary arteries from the lungs to the heart?

Answers

Yes,oxygen-rich blood is carried through pulmonary arteries from the lungs to the heart.

It is false that oxygen-rich blood is carried through pulmonary arteries from the lungs to the heart.

What is pulmonary artery?

The two principal arteries leaving the right ventricle of the heart are known as the pulmonary arteries. Low-oxygen blood is seen in this lower chamber of the heart. This blood travels to the lungs through the pulmonary arteries.

The middle mediastinum contains the main pulmonary artery, as well as the pulmonary arteries that follow on the right and left. They emerge from the four chambered heart's right ventricle and carry blood to the lungs.

Right side of heart sends deoxygenated blood to pulmonary artery. Nature has made it such that this blood reaches the lungs where carbon dioxide can be released and then oxygen can be loaded.

It is true that all arteries convey oxygenated blood, with the exception of the pulmonary artery.

Thus, the given statement is false.

For more details regarding pulmonary artery, visit:

https://brainly.com/question/4385723

#SPJ6

Other Questions
Which is the equation of the line that passes through the points (4, 3) and (6, 2)? What is the value of the expression401P + q?), when p = 49 and q = -2?O A) 12OB) 20OC) 36OD) 44First person to answer will get 10 points :D Please help Im failing and I need to bring it up 1.[tex]16 \frac{3n}{4} \div 18 \frac{5n}{4} \times {4}^{n + 2} [/tex]simplify2.[tex] {2}^{2y} = 6( {2}^{y)} - 8[/tex]Find the value for y3.[tex] {2}^{2x + 1} - 15( {2}^{x}) - 8 = 0[/tex]Solve the equation I will mark you brainliest Estimate a 15% tip for a $26.40 restaurant billa) $1.50b) $6.00c) $8.00d) $4.00 Lindas aunt zoe charges her a nominal amount for watching her two children aunt zoe charges $2.50 per day plus $1.75 per hour one day linda paid her aunt $14.75 how many hours did aunt zoe watch the children what changed do you think would happen as a result of Earths orbit decreasing in size? How do you do this equation? 2(m+7)= blank m+ blankUse properties of operations to complete the equivalent expression. How much power is required to carry a 35Npackage a vertical distance of 18 m if the work onthe package is accomplished in 30 s? Help ASAP nowwwwww Please and thank you Can someone please help me, click on the link to see the question. The percentage of members from slave states was __________ percent in 1800 and__________ percent in 1850. PLZ HELP WILL GIVE BRAINLIST IF CORECT!!! How do the characteristics of an organism contribute to their survival? Where on the periodic table are metal elements most likely found?A. Along the stairstep lineB. In the main groupsC. On the left sideD. On the right side What is the common denominator for 7 and 2 Plzzzzzzzzzzzzzzzz helllppppppp meeeeeeeeee PLEASE I NEED HELP QUICK !!!! What two revisions would correct the parallelism errors in the sentence? All journalists must be without bias to be successful.TrueFalse Which of the following is an example of a physical change?