How would I find the interval of convergence for the following series: i) $\displaystyle \sum \frac{(x+2)^n}{n^2}$ ii)$\displaystyle \sum \frac{(-1)^kk^3}{3^k}(x-1)^k^+^1$ iii)$\displaystyle \sum (1+\frac{1}{n})^nx^n$
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Have you tried some convergence tests like the ratio test and the root test? It looks like the root test would work well for (iii) and the ratio test for (i) and (ii). - Hollywood
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