What is the sum from k=1 to infinity of (k!)/(104^k) ?

The sum from k=1 to infinity of (k!)/(104^k) is diverges

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sum from k=1 to infinity of (k!)/(104^k)

k = 1 \sum \infty \frac{k !}{10 4 ^{k}}

diverges

Solution steps

k = 1 \sum \infty \frac{k !}{10 4 ^{k}}

Apply Series Ratio Test:

diverges

= diverges

n = 1 \sum \infty n arctan (\frac{1}{n})

n = 2 \sum \infty (\frac{3}{7})^{4 n}

n = 1 \sum \infty \frac{2 ( - 1 ) ^{n}}{n}

n = 1 \sum \infty \frac{6 n}{4 n + 1}

n = 1 \sum \infty \frac{2}{5 n ^{2} + 5 n}

What is the sum from k=1 to infinity of (k!)/(104^k) ?
The sum from k=1 to infinity of (k!)/(104^k) is diverges