Find the radius of convergence and interval of convergence for the given series $$\sum_{n}^{\infty}{n^n(x+3)^n}/(n^{100}+100n+29)$$ I'm trying to use the ratio test to find the radius of convergence $R$ and the interval of convergence $I$, but I'm stuck on how to set up the problem, i.e. should $n^n$ turn into $n^{n+1}$ or $(n+1)^{n+1}$ (I believe its the latter). And if so then what terms cancel? And if I ends up being more than one number what endpoints converge/diverge?
2026-04-11 23:55:53.1775951753
Find the radius of convergence and interval of convergence for the given series $\sum_{n}^{\infty}{n^n(x+3)^n}/(n^{100}+100n+29)$
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By using the ratio test and since we have $$\lim_{n\to \infty}{(n+1)^{n+1}\over n^{n}}{= \lim_{n\to \infty}{(n+1)^{n}\cdot (n+1)\over n^{n}} \\=\lim_{n\to \infty}\left({1+{1\over n}}\right)^n(n+1) \\=\lim_{n\to \infty}e(n+1) \\=\infty }$$then the radius of convergence is $0$.