Lebl-Basic-Analysis-I · Problem 2.6.1

Sequences and Series

Mathematics · series-convergence-divergence

Problem

Decide the convergence or divergence of the following series. a) ∑n=1∞122n+1\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^{2n+1}} b) ∑n=1∞(−1)n(n−1)n\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^n(n-1)}{n} c) ∑n=1∞(−1)nn1/10\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^n}{n^{1/10}} d) ∑n=1∞nn(n+1)2n\displaystyle\sum_{n=1}^{\infty} \frac{n^n}{(n+1)^{2n}}

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