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find the value of x for which the series converges sigma (x+7)^n for n=1 to n=infinity

find the value of x for which the series converges

sigma (x+7)^n for n=1 to n=infinity

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Answer #1

According to ratio test, let be a given series. The series converges if p<1 where

Here the series is

  

  

For the series to be convergent, p<1.

So, for the value of x from -8 to -6, the series converges.

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