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Ratio test
Task number: 2932
Investigate the convergence of the series
Variant 1
∞∑n=11n!.
Variant 2
\displaystyle \sum\limits_{n=1}^{\infty} \frac{2^n}{n!}.
Variant 3
\displaystyle \sum\limits_{n=1}^{\infty} \frac{n!}{2^{n^2}}.
Variant 4
\displaystyle \sum\limits_{n=1}^{\infty} \binom{2n}n \frac{1}{5^n}.
Variant 5
\displaystyle \sum_{n=1}^{\infty}\frac{2^nn!}{n^n} .
Variant 6
\displaystyle \sum_{n=1}^{\infty}\frac{3^nn!}{n^n} .
Variant 7
\displaystyle \sum_{n=1}^{\infty}\frac{(2n)!}{(n!)^2} .
Variant 8
\displaystyle \sum_{n=1}^{\infty}\frac{n^n}{(2n)!}.