Friday, 11 September 2015

real analysis - Checking convergence of a sequence

For n1, is the sequence (xn)n=1 where:
xn=1+12+...+1n2n

convergent?



I started with xn+1xn=n(n+1)(2n+1)n+10 since geometric mean does not exceed algebraic mean, thus decreasing, but what about convergence?

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