What is the sum from k=1 to infinity of (k!)/(105^k) ?

The sum from k=1 to infinity of (k!)/(105^k) is diverges

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sum from k=1 to infinity of (k!)/(105^k)

k = 1 \sum \infty \frac{k !}{10 5 ^{k}}

diverges

Solution steps

k = 1 \sum \infty \frac{k !}{10 5 ^{k}}

Apply Series Ratio Test:

diverges

= diverges

k = 0 \sum \infty (- \frac{4}{5})^{k}

n = 0 \sum \infty 7 (\frac{4}{5})^{n}

n = 1 \sum \infty \frac{n ^{2}}{8 ^{n}}

n = 1 \sum \infty \frac{9 ^{n}}{n + 1}

What is the sum from k=1 to infinity of (k!)/(105^k) ?
The sum from k=1 to infinity of (k!)/(105^k) is diverges