Consider the series One-fourth, StartFraction 1 Over 16 EndFraction + StartFraction 1 Over 64 EndFraction + StartFraction 1 Over 256 EndFraction + ellipsis
Which expression defines Sn?
Answers
Answer:
C, I got it right
Step-by-step explanation:
The two major types of series are the arithmetic series and the geometric series. The arithmetic series is characterized by common difference, while the geometric series has common ratio between two successive terms.
The sum of the given series is:
[tex]\lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
The given series is a geometric series. So, we first calculate the common ratio (r) using:
[tex]r = T_2 \div T_1[/tex]
From the series, we have:
[tex]T_1 = \frac{1}{4}[/tex]
[tex]T_2 = \frac{1}{16}[/tex]
So, the equation becomes
[tex]r = \frac{1}{16} \div \frac{1}{4}[/tex]
Rewrite as product
[tex]r = \frac{1}{16} * \frac{4}{1}[/tex]
[tex]r = \frac{1}{4}[/tex]
The formula to calculate the sum of a geometric series of is:
[tex]S_n = \frac{a(1 - r^n )}{1-r}[/tex]
Where
[tex]a = T_1 =\frac{1}{4}[/tex] -- the first term
[tex]S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{1-\frac{1}{4}}[/tex]
Simplify the denominator
[tex]S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{\frac{3}{4}}[/tex]
Divide 1/4 by 3/4
[tex]S_n = \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
We can conclude that, the sum of the series is:
[tex]S_n = \lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
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Related Questions
Please assist me in the geometry please !!!!
Answers
Answer:
Solution given:
length of cube[a]=6ft
volume of cube =a³=6³=216ft³
again
For cylinder
d=4ft
r=2ft
h=6ft
volume of cylinder=πr²h=π×2²×6=75.4ft³
Now
remaining volume=216-75.4=140.6ft³
is a required answer.
Which equation matches y = 2x + 3
a) The cost of buying two shirts after a $3 discount
b) The total amount of money you make after spending $3 on
supplies and selling for $2 per item
c) The total height of a 3 inch tree after it grows 2 inches per
month.
d) The amount of money in your bank account if you started
with $2 and make $3 per day.
Answers
The total height of a 3 inch tree after it grows 2 inches per month
The equation y=2x+3 matches the total height of a 3-inch tree after it grows 2 inches per month.
We have given, y=2x+3
We have to determine whether the equation matches y=2x+3.
What is the slope-intercept form?
The slope-intercept form of the line is y=mx+c.
Where m is the slope
C=y-intercept
Therefore option c is correct.
because the height is three inches and the tree after it grows 2 inches per month.
The slope of a line is a measure of its steepness.
Here the slope is 2 and the y-intercept is 3.
Therefore option c is correct.
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What is -0.032 + 6.42 ?
Answers
Answer:
6.388
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
6.38800
Step-by-step explanation:
Find the missing value so that the line passing through the 2 points has the given slope.
(-7,-3) and (-1. y); slope: 1
Answers
Answer:
3
Step-by-step explanation:
We know that the slope of a line passing through the points ( x ₁ , y₁) and ( x₂ , y₂ ) is ,
→ Slope ( m ) = ( y₂ - y₁) / ( x₂ - x ₁ )
The points here are (-7,-3) and (-1,y) . Using formula of the slope , we have ,→ m = -3 - y / -7 - (-1)
→ 1 = -(3+y)/ -7+1
→ 1 = -(3+y) / -6
→ 6 = 3 + y
→ y = 6 - 3
→ y = 3
Hence the value of y is 3 .list all the factors of 10
Answers
Answer: factors of 10 are 1, 2, 5, and 10.
Step-by-step explanation: You can also look at this the other way around: if you can multiply two whole numbers to create a third number, those two numbers are factors of the third. 2 x 5 = 10, so 2 and 5 are factors of 10.
Answer:
1,2,5,10
Step-by-step explanation:
1 x 10 = 10
2 x 5 = 10
10 x 1 = 10
SOMEONE PLEASE HELP
Answers
Answer:
the answer is 20.
Step-by-step explanation:
I hope that helps
Answer:
20
Step-by-step explanation:
(estimation)
help pls at least some °ω°
Answers
2.4 x 6 = 14.4
5.3 x 7 = 37.1
7.2 x 8 = 57.6
5.1 x 9 = 45.9
i did the entire first row
Answer:
12.5
14.4
37.1
57.6
45.9
71.1
77.4
70.4
60
59.4
47.6
34.2
48.3
67.5
75.6
No joke answers. No links. Will award BRAINLIEST if correct!!Question 12 (1 point)
A scientist is interested in whether stretching before running 5 kilometers will improve a runner's time. The
scientist decides that an experimental study is the best method to use to answer the question. One group of
runners will run a 5-kilometer race without stretching, and a second group of runners will follow a specific
stretching routine before running the race. The finishing times will be recorded, along with the group type for
each runner
The group that raced without stretching has a mean finish time of 23.5 minutes and a standard deviation of 2.6
minutes. Write a sentence or two that summarizes any conclusions that can be made about the statistical
question, "Does stretching before running a race improve a runner's time?"
Answers
Answer:
Yes
Step-by-step explanation:
A quadrilateral has the following vertices on a coordinate plane:
Point J: (3,−6)
Point K: (−1,−6)
Point L: (−1,2)
Point M: (3,2)
Enter the length of side JK.
units
Answers
Answer:
We have to draw it!
Step-by-step explanation:
Use graph paper:
4 units i graphed it out
Find the volume of the rectangular prism.
11 cm
11 cm
11 cm
Volume
[?] cm
cm
Answers
Answer: 1331
Step-by-step explanation: v=lwh
The volume would be 1,331 cm cubed. I hope this helps, have a good day!
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 84 ounces of strawberry infused water
Answers
Answer:
21 ounces of juice.
63 ounces of water
Step-by-step explanation:
let :
x = ounces of strawberry juice to make the strawberry infused water.
3x = ounces of water needed to make the strawberry infused water.
3x + x = 84
4x = 84
divide both sides of the equation by 4
x = 21 ounces
3x = 3 x 21 = 63 ounces
Can someone plz help me?
Answers
Answer:
c
Step-by-step explanation:
c
875 × 36 I'll crown and give five stars if you say the solving steps
Answers
Answer:
31500
Step-by-step explanation:
h t t p s://www.y o utube.com/watch?v=sSqJQVjkgBM
Dk how to do this can sm1 explain
Answers
[tex]V = \frac{4}{3}\pi r^3\\r^3 = \frac{3V}{4\pi}\\r = \sqrt[3]{\frac{3V}{4\pi}}[/tex]
[tex]r = \sqrt[3]{\frac{3*36\pi}{4\pi}} = \sqrt[3]{3*9} = \sqrt[3]{27} = 3[/tex] m
Answer: B (3 m).
36π = πr²
Divide both side by π
36π/π= πr²/π
36 = r²
r = 6
What percent of the people surveyed more than 10 hours of exercising each week?
Answers
Answer:
The percentage of people is 60%
Step-by-step explanation:
The reasoning this is the answer is because you to find the percentage you take the amount which does the thing or the part of the whole which is included in the slection ad you divide it by the total and multiply that by 100 so (2100/3500)*100 and that gives you 60%
Solve the system of equations by
graphing.
y = 2x - 5
2y - 4x = 4
And find solution.
Help is greatly appreciated
Answers
Answer:
I need help with that as well, if you could tell me the answer please and the top as well
Step-by-step explanation:
Question 10 (10 points)
It cost Joe Chavez a total of $200 to rent a car. He drove the car 850 miles. What was his cost per mile?
O a
Ob
Ос
Od
$0.18
$0.25
$0.87
$0.24
Answers
Answer:
the answer is certainly A
Factor the following polynomial with the greatest common factor
Answers
Answer:
6x³(2x - x² + 3)
Step-by-step explanation:
Given
12[tex]x^{4}[/tex] - 6[tex]x^{5}[/tex] + 18x³ ← factor out 6x³ from each term
= 6x³(2x - x² + 3)
Find the value of Sin^-1(-√3/2)
Answers
Answer:
The exact value of sin-1(√32) sin -1 ( 3 2 ) is π3 .
Step-by-step explanation:
A windshield wiper is 18 inches long and its blade is 12 inches long. It sweeps through an angle of 130 degrees. What is the total area wiped by the windshield wiper?
Answers
Answer:
[tex]A=65 inches^2[/tex]
Step-by-step explanation:
From the question we are told that:
Length of wiper [tex]x=18[/tex]
Length of blade [tex]y=12[/tex]
Angle[tex]\theta=130\textdegree[/tex]
Generally the equation for Cover Area windshield wiper A_w is mathematically given by
[tex]A_w=x^2*\frac{\theta}{360}[/tex]
[tex]A_w=18^2*\frac{130}{360}[/tex]
[tex]A_w=117 \textdegree[/tex]
Generally the equation for Cover Area windshield blade A_b is mathematically given by
[tex]A_b=y^2*\frac{\theta}{360}[/tex]
[tex]A_b=12^2*\frac{130}{360}[/tex]
[tex]A_b=52 \textdegree[/tex]
Therefore total Area wiped by windshield wiper A
[tex]A=A_w-A_b[/tex]
[tex]A=65 inches^2[/tex]
please help, ill mark brainliest = )
Answers
Answer:
1.6lb
30oz
800g
Step-by-step explanation:
That's the order.
help me please for points
Answers
Answer:
B
Step-by-step explanation:
40-2n
when n=2
simply replace n with 2
therefore we have
=40-2(2)
=40-4
answer=36
Complete the table of values for y = x2 - 4x
Answers
Answer:
y = -2x
Step-by-step explanation:
hhahahahhahaha hehe looking for my points
Answer a b c and d ?pls
Answers
Non-examples of least Common Multiple
Answers
Answer:
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
Step-by-step explanation:
If two numbers have no common factors greater than 1, then their LCM will be their product. For example, take numbers 7 and 9. They have none common factor greater than 1. So, LCM will be 7 * 9 = 63.
Max is taking a cab in New York City. The fare is calculated as a base charge of $3.00 plus an additional $2.00 per mile traveled. It is also customary to leave a $2 tip.If Max wants to spend exactly $20, how many miles can he travel?
Answers
Answer: 7.5miles
Step-by-step explanation:
Since the fare is calculated as a base charge of $3.00 plus an additional $2.00 per mile traveled and also customary to leave a $2 tip and Max wants to spend exactly $20. This information can be formed into an equation as:
Let the miles that he can travel be m.
3 + (2 × m) + 2 = 20
3 + 2m + 2 = 20
5 + 2m = 20
2m = 20 - 5
2m = 15
m = 15/2
m = 7.5miles
Therefore, Max can travel 7.5miles
you go for a run on monday you ran 1.23km on tuesday you ran the same distance , how far did you run altogether ?
Answers
B) Redville is directly west of Yellowton, and Purplesburg is 151 miles directly north of Redville. If Yellowton is 258 miles from Purplesburg, how far is Redville from Yellowton in miles? Round to the
nearest tenths, if necessray.
B) answer: miles
Answers
Answer:
is that for social studeies
Step-by-step explanation:
Someone help me with this pls
Answers
(5^-2)^2 and 5^2•5^-6
a cylinder and a cone have the same volume. the cylinder has a radius x and height y. the cone has a radius of 1/2 x. find the height of the cone in terms of y.
URGENT PLS
Answers
Answer:
12 y
Step-by-step explanation:
π. x².y = ⅓. π (½x) ².h
=> eliminate π,
x²y = ⅓. ¼x².h
=> eliminate x²,
y = 1/12 h
h = 12 y
so, height of the cone = 12 y