why is $\sum (-1)^{n+1} n^{1/n}$ is not converging? What is meant by convergence here, is the value does not stay firm?
2026-04-12 01:19:10.1775956750
$\sum (-1)^{n+1} n^{1/n} $ is not converging?
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Apparently IT IS NOT converging as the general term $$ a_n=(-1)^{n+1}n^{1/n}, $$ DOES NOT converge to zero.
Note. An alternating series, such as the one in the OP, converges provided that the underlying sequence is positive, decreasing and tends to zero.