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).

Solutions

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 : .

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


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