Answer to Question #17566 in Real Analysis for Divya wadhwa

Question #17566
Determine whether the series converges. summation[1/{n+(-1)^n}^2]
1
Expert's answer
2012-10-31T08:36:30-0400
Let us show that the series converges.
It is well known that the series summation[ 4/n^2] converges
Since n/2 <n+(-1)^n for n>2, we get that 1/{n+(-1)^n}^2 < 4/n^2, and so
summation[1/{n+(-1)^n}^2] < summation[ 4/n^2 ] < infinity
Hence the series summation[1/{n+(-1)^n}^2] converges.

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