Consider the following series.

1/4 + 1/8 + 1+12 + 1/16 + 1/20.....

Required:
Determine whether the geometric series is convergent or divergent.

Answers

Answer 1

Answer:

The series is convergent.

Step-by-step explanation:

1/4 + 1/8 + 1+12 + 1/16 + 1/20

In each term, the numerator stays 1, while the denominator is multiplied by 4. Thus, the series is given by:

[tex]\sum_{n=1}^{\infty} \frac{1}{4n}[/tex]

Convergence test:

We compare the sequence of this test, [tex]f_n = \frac{1}{4n}[/tex], with a sequence [tex]g_n = \frac{1}{n}[/tex].

If [tex]\lim_{n \rightarrow \infty} \frac{f_n}{g_n} \neq 0[/tex], the series is convergent. So

[tex]\lim_{n \rightarrow \infty} \frac{f_n}{g_n} = \lim_{n \rightarrow \infty} \frac{\frac{1}{4n}}{\frac{1}{n}} =  \lim_{n \rightarrow \infty} \frac{n}{4n} = \lim_{n \rightarrow \infty} \frac{1}{4} = \frac{1}{4} \neq 0[/tex]

As the limit is different of zero, the series is convergent.


Related Questions

The Pythagorean Identity states that (sin x)^2 + (cos x)^2 = 1 Given cos 0 = 7/4 find sin 0. Simplify the fraction.

Answers

Answer:

sin∅=3/4

Step-by-step explanation:

sin²x+cos²x=1

sin²x+(√7/4)²=1

sin²x+7/16=1

sin²x=9/16

sinx=3/4

Therefore, sin∅=3/4

The Unit Circle

What is the period for the graph of y = cos(∅)? (Sketch a graph to help determine the answer)

a. 180°
b. 90°
c. 360°
d. 270°

Please select the best answer from the choices provided

Answers

Answer:

C. 360°

Step-by-step explanation:

I calculated it logically

Answer:

Answer is C) 360°

Step-by-step explanation:

find the difference between 0.1 kg and 75g​

Answers

Answer:

25 g

Step-by-step explanation:

0.1 kg can be written as 100 grams

& 75 g

while 1 kg is 1000 grams

so difference:-

(100- 75 ) grams

= 25 g

The difference between 0.1 kg and 75 g is 25 grams. To find the difference between 0.1 kg and 75g, you need to make sure both quantities have the same unit.

Since 1 kg is equal to 1000 g, you can convert 0.1 kg to grams:

0.1 kg = 0.1 * 1000 g = 100 g

Now, the two quantities are in the same unit:

0.1 kg - 75 g = 100 g - 75 g = 25 g

So, the difference between 0.1 kg and 75 g is 25 grams.

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What is the probability that I will roll a 4 on a standard number cube?

Answers

Answer:

the probability of rolling any single digit on a 6-sided fair cube is 1/6

To roll a 4 on a standard number cube is 1/6

If there is a $50 profit on the large cabinets and a $30 profit on the small cabinets.
What number of large and small cabinets maximizes the objective function?
P = 50x + 30y
a) o large and 10 small
b) 8 large and small
c) 4 large and small
d) 4 large and 5 small

Answers

Answer: B

Step-by-step explanation: I hope I am good at math if not sorry

The combination of 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640. Option b is correct.

To maximize the objective function P = 50x + 30y, where x represents the number of large cabinets and y represents the number of small cabinets.

Need to determine the combination of x and y that results in the highest value for P.

For 0 large and 10 small:

P = 50(0) + 30(10)

= 0 + 300

= 300

For 8 large and 8 small:

P = 50(8) + 30(8)

= 400 + 240

= 640

For 4 large and 4 small:

P = 50(4) + 30(4)

= 200 + 120

= 320

For 4 large and 5 small:

P = 50(4) + 30(5)

= 200 + 150

= 350

Based on these calculations, 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640.

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Find the area of the shaded region in the drawing round to the nearest tenth show all work

Answers

Answer:

The area of the shaded region is:

488 ft^2.

Step-by-step explanation:

First, we're gonna find the area of the whole rectangle and next we can subtract the area of the triangles in the corners, we use the next formula:

Area of a rectangle = width * heigth

And we replace the measurements in the picture (32 ft and 16 ft):

Area of a rectangle = 16 ft * 32 ftArea of a rectangle = 512 ft^2

Now, we must calculate the area of a triangle, this can be made by this formula:

Area of a triangle = (base * height) / 2

We can replace the values we have in the picture (4 ft and 6 ft), then:

Area of a triangle = (4 ft * 6 ft) / 2Area of a triangle = (24 ft^2)/ 2Area of a triangle = 12 ft^2

As you can see in the picture, we have to subtract two triangles with the same measurements, by this reason, we multiply the area of the triangle by two and we'll obtain the area we must subtract:

Area to subtract = (12 ft^2) * 2Area to subtract = 24 ft^2

At last, we take the area of the whole rectangle and subtract the area of the triangles:

Area of the shaded region = 512 ft^2 - 24 ft^2Area of the shaded region = 488 ft^2

The area of the shaded region is 488 ft^2.

Construction crews are building a highway between the towns of Washington and Jefferson. Currently the highway is 16.25 miles long. Each month the total length increases by 4.5 miles. Which equation can be used to find y, the total length of the highway in miles after x months?

Answers

Chuckinghchchdd underhand drop ribbon stucco Tio stain stucco during

Simplify the expression:
9f2 - 10 - 1 + 2/2 + -772​

Answers

Answer:

4f^2-11

Step-by-step explanation:

HELP THANK YOU SM !!! ​

Answers

Answer:

Your answer is C

Step-by-step explanation:

Katy put $3000 into his bank account.  If the account pays 6% interest compounded continuously, when will it be worth $6000?   Round to 3 decimal places.​

Answers

Answer:

11.55 years

Step-by-step explanation:

Given data

Principal= $3000

Rate= 6%

Final Amount= $6000

expression for the time is given as

t = ln(A/P) / r

Substitute

t= ln(6000/3000)/0.06

t= ln(2)/0.06

t= 0.693/0.06

t= 11.55 years

Hence the time is 11.55 years

Use formulas to find area

Answers

120.08 u just had to multiply

Answer:

120.08

Step-by-step explanation:

15.8 x 7.6

-> 120.08 [tex]m^2\\[/tex]

A sixth grade class recorded the number of letters in each students first name. The results are shown in the dot plot. Which is the best representation of the center of this data set?

Answers

Answer:

the center of the data set is 7 so probably 7

7 is the best representation of the center of given data set.

The correct answer is an option (C).

What is center of data?"It is the middle of a distribution.""Mostly, The measures of the center of the data are the mean and the median."What is mean?

"It is the average of the given numbers."

What is median?

"I is the middle value of a sorted list of numbers."

For given question,

We have been given a dot plot of the number of letters in each students first name.

From the given dot plot,

We have data as 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11

From above data,

the total number of students in the class are n = 30

We write 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11 as 3, (4 × 2), (5 × 4), (6 × 7), (7 × 7), (8 × 3), 9, (10 × 2), (11 × 3)

So, the mean of the above data would be,

[tex]\Rightarrow \bar{X}=\frac{3+ (4\times 2)+(5\times 4)+(6\times 7)+(7\times 7)+(8\times 3)+9+(10\times 2)+(11\times 3)}{30}\\\\\Rightarrow \bar{X}=\frac{208}{30}\\\\\Rightarrow \bar{X}=6.93\\\\\Rightarrow \bar{X}\approx 7[/tex]

From above data we can observe that there are two numbers in middle of the data 6 and 7.

So, the median would be,

[tex]\Rightarrow M=\frac{6+7}{2}\\\\\Rightarrow M=6.5\\\\\Rightarrow M\approx 7[/tex]

Therefore, 7 is the best representation of the center of given data set.

The correct answer is an option (C).

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If 4 is subtracted from a certain number and the difference is divided by 4, the result is 1 more than 1/6 of the original number. Find the original number

Answers

Answer:

Step-by-step explanation:

x-4/4=x/6+1

x-4 =4/6x+4

x-2/3x =8

1/3x =8

x=24

If the graph of y = - x ^ 2 translated horizontally 7 units to the right and translated vertically 6 units upwards, what’s the new equation?

Answers

9514 1404 393

Answer:

  y = -(x -7)² +6

Step-by-step explanation:

Replacing x with (x-h) translates the graph h units to the right. You want h=7.

Replacing f(x) with f(x)+k translates the graph k units upward. You want k=6.

These transformations make the new equation be ...

  y = -(x -7)² +6

i need assistance please

Answers

i got 22%! hope this helps

Comprehension Question
Answer the question correctly for 30 dollars.

Read the sentence from paragraph 2.

If we continue throwing plastic bags in the garbage, our landfills will become towering mountains of trash.

What does this sentence show?


.A. the author’s use of humor to change the tone of the passage

B. the author’s use of exaggeration to make a point about landfills

C. the author’s use of details to support his argument for paper bags

D. the author’s use of description to provide personal experience on the topic

Answers

Answer:

B.

Step-by-step explanation:

Our landfills will not actually become towering mountains of trash, that's just a hyperbole used by the author to show the destructive impact that trash in large quantities can have.

struggling with homework!!

Answers

Answer:

40

Step-by-step explanation:

if 20% were Caesar and 20 divided by 5 is 4, then every four salads sold is five percent.

The table below represents which equation ?

Answers

Answer:

D

Step-by-step explanation:

Find the slope by picking two ordered pairs in the table and using the slope formula( y2-y1/x2-x1) to get the slope. The smallest numbers are easiest to work with. (-1,1), (0,-2)

-2-1/0-(-1) = 3/0+1 = -3/1 = m=-3

Use one of the points you used and plug in the x and y values of the ordered pair into the equation with the slope to find your b( y-intercept). (0,-2)

-2= -3(0) +b

-2= 0+b

b=-2

The final equation will only have your slope and b( y-intercept). That should be your answer. Hope this helps!

Final Equation: y=-3x-2

Can somebody recommend me some horror, psychological, yandere, and/or thriller anime?

Anything besides these would be appreciated:

1. Angels of Death
2. Shiki
3. Re:Zero
4. Corpse Party
5. Magical Girl Site
6. Happy Sugar Life
7. SCHOOL-LIVE!
8. Talentless Nana
9. Higurashi
10. Wonder Egg Priority
11. Shadows House
12. Blood C
13. To Your Eternity
14. Puella Magi Madoka Magica
15. Another
16. The Lost Village
17. Serial Experiments Lain
18. Chaos;Head

Answers

Answer:

the future diary  

Step-by-step explanation:

I watched Future Diary on Hulu, its a really good anime, its more of a yandere type of anime, hope you enjoy it!

geometry help pleaseeee

Answers

Answer: 11

Step-by-step explanation:

[tex]48=4x+4[/tex] (angles opposite congruent sides in a triangle are congruent)

This gives that x = 11

What voltage is required to force 4.5 amperes of current through an electric iron having a resistance of 25.5 ohms

Answers

Answer:

V = 114.75 Volts

Step-by-step explanation:

Ohm's Law   V = IR

I = 4.5 A

R = 25.5 Ω

V = (4.5)(25.5)

V = [4×25.5] + [0.5×25.5]

V =  102 + 12.75

V = 114.75 Volts

Is the answer A, B, C, or D?

Answers

Answer:

A

Step-by-step explanation:

2 3/8=19/8=2.375

Somebody Please help!!!

Answers

Answer:

176

Step-by-step explanation:

8+8+64+64+16+16

Julie started her own lawn mowing business to earn some extra money last
summer. She earned $2100 and had expenses of $669 (lawn mower, weed
eater, gas, etc.). She has no income to report on line 1a or line 1b of
schedule SE below. She also has a zero entry on line 29 of Form 1040. Use
this information to complete table entry 3 below. *

Answers

2100 is the answer I think

Two parallel lines are cut by a transversal. What is the measure of <1?

A 80
В. 180
C. 100
D. 90

Answers

Answer:

C - 100

Step-by-step explanation:

9514 1404 393

Answer:

  C.  100°

Step-by-step explanation:

Consecutive (same-side) exterior angles are supplementary.

  ∠1 = 180° -∠7 = 180° -80°

  ∠1 = 100°

What is the solution to the equation √8x = √4+2x?

Answers

Answer and Step-by-step explanation:

The first step in solving for x is to square both sides.

8x = 4 + 2x

Now, subtract 2x from both sides.

6x = 4

Now, divide each side by 6.

x = [tex]\frac{4}{6} = \frac{2}{3}[/tex]

x = [tex]\frac{2}3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

No links please 15 Points

Answers

Answer:

C

Step-by-step explanation:

I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS
please help this is very important
this is a big part of my grade

Answers

the answer is d !! have a good day

Answer:

pretty sure the answer is electrons  so D

Step-by-step explanation:

Electrons are particles that surround the nucleus of an atom like a cloud

The base of the sandbox is shaped like a parallelogram. He parallelogram base has an area of 9 square feet and the sand box gas a volume of 13.5 cubic feet. What is the height of the sandbox?

Answers

Answer:

1.5 feet

Step-by-step explanation:

V = base area x height

divide the two members by the base area

height = V/ base area

height = 13.5 / 9 = 1.5 feet

what is 2+2 4+4 8+8 i need math help

Answers

Answer:

2+2 is 4 4+4 is 8 8+8 is 16

Step-by-step explanation:

if you need them added up here: 4+8 =12 12+16 = 28

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