1.II.9F

Analysis | Part IA, 2005

Examine each of the following series and determine whether or not they converge.

Give reasons in each case.

(i)(i)

(ii)(i i)

n=11n2+(1)n+12n+1\sum_{n=1}^{\infty} \frac{1}{n^{2}+(-1)^{n+1} 2 n+1}

(iii)

n=1n3+(1)n8n2+1n4+(1)n+1n2\sum_{n=1}^{\infty} \frac{n^{3}+(-1)^{n} 8 n^{2}+1}{n^{4}+(-1)^{n+1} n^{2}}

(iv)(i v)

n=1n3een\sum_{n=1}^{\infty} \frac{n^{3}}{e^{e^{n}}}

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