Question

In: Advanced Math

1. a.) Find the values of x for which the series converges. Express your answer in...

1. a.) Find the values of x for which the series converges. Express your answer in interval notation. n = 1 ∞ ∑(−3)ⁿ?ⁿ

b.) Find the sum of the series (valid over the values of x found in part a).

Expert Solution

1.

(a). Given series .

If be the radius of convegence of the above series then ,

Now at the series is which is an divergent series .

At the series is which is an divergent series .

Hence the interval of convergence of the given series is .

Answer : .

(b). Sum of the series ,

, which is an geometric series with common ratio -3x .

, as .

Hence the required sumof the series is .

Answer : .

.

If you have doubt or need more clarification at any step please comment .

Colby Messinger answered 6 months ago

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1. a.) Find the values of x for which the series converges. Express your answer in...

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