Find the value of x for which the series converges. Then Find the sum of the serises for those values of x

infinite series

2^n(x+1)^n

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- Nov 3rd 2008, 08:11 PMamiv4When does the series converge
Find the value of x for which the series converges. Then Find the sum of the serises for those values of x

infinite series

2^n(x+1)^n - Nov 3rd 2008, 08:21 PMJameson
You can combine those terms under the same power since they are being multiplied.

$\displaystyle [2(x+1)]^n$

This is a geometric series and converges for a^n, whenever a<1. So 2(x+1)<1 for this to converge.