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Arturiano [62]
1 year ago
8

Find all values of x for which the series converges. (enter your answer using interval notation. ) [infinity] (4x)n n = 1

Mathematics
1 answer:
andreyandreev [35.5K]1 year ago
8 0

The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ 9x^{n} x^{n}

We have to find the values of x for which the series converges.

We know,                

∑ ar^{n-1}    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ (9x)^{n} is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

For more information about convergence of series, visit

brainly.com/question/15415793

#SPJ4

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djverab [1.8K]

Answer:

2x

Step-by-step explanation:

Solve the equation for a as follows:

First multiply both sides by 2a:

(2a)x=-b and then divide both sides by 2x:

a=-\frac{b}{2x}

3 0
3 years ago
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What is the range for this data set?<br> 22, 7, 14, 13, 38, 12, 19, <br> 17, 49, 13, 9, 18, 36​
Degger [83]

Answer:

from 7 to 49 or (7, 49)

Step-by-step explanation:

Range means the limit of the data set. Basically, the low part of the range is the lowest number in the set and the high part of range is the highest part.

5 0
2 years ago
Len has 3 strips of construction paper. Each strip is the same size and a different color-red, yellow, and pink. He tapes the st
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Answer:

2/6

Step-by-step explanation:

Each of the rectangle strips are taped together to form a rectangle. Therefore 1 of the third of the rectangle would be red, this means that 1/3 of the rectangle would be red color. The rectangle is then divide into sixths, this can be achieved by dividing each of the taped strip into 2.

Therefore 2 of the sixths rectangle would be red in color, Hence the fraction of the rectangle that would be red is given as 2/6

7 0
2 years ago
1.
Olegator [25]
Hope this helps somewhat

7 0
3 years ago
How many times can 2 1/2 be subtracted from 12 1/2
Luba_88 [7]
2 1/2 = 2.5
12 1/2 = 12.5

This means you can calculate how may times it goes in by dividing it and rounding the number down:

12.5 / 2.5 = 5

*5 can not be rounded down so it stays the same

This means that 2 1/2 goes into 12 1/2 5 times. Hope this helps! :)
5 0
3 years ago
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