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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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.
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