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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