Jerold
2021-03-05
Answered

Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges.

$\frac{9}{100}+\frac{9}{{100}^{2}}+\frac{9}{{100}^{3}}+...+\frac{9}{{100}^{n}}+...$

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saiyansruleA

Answered 2021-03-06
Author has **110** answers

Given data

The series is:

Consider the infinite series and compare with it given series,

The nth partial sum of the given series is,

The first term of the given series is:

The common ratio is:

The expression for the sum of series is,

Substitute the values in the above expression,

Thus the formula for nth partial sum of series is

The expression for the limit of the nth partial sum of the given series is,

The nth partial sum of the given series is

Thus the sum of the series is

Jeffrey Jordon

Answered 2021-12-16
Author has **2313** answers

Answer is given below (on video)

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