Does $\sum\limits_{n=1}^{\infty} k^{1/n}$ converge when $k<1$ ??? How to show whether it does or does not then? Integral test or comparison test with $k^n$ does not seem to work.
2026-03-27 22:18:58.1774649938
Convergence of $\sum\limits_{n=1}^{\infty} k^{1/n}$
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If $\displaystyle \sum a_n$ converges, it is necessary that $a_n \rightarrow 0$. What is $\displaystyle \lim_{n \rightarrow \infty} 1/n$? Given that $k^x$ is continuous, what is $\displaystyle \lim_{n \rightarrow \infty} k^{1/n}$?