What is the sum from n=0 to infinity of (n!)/(7^n) ?

The sum from n=0 to infinity of (n!)/(7^n) is diverges

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sum from n=0 to infinity of (n!)/(7^n)

n = 0 \sum \infty \frac{n !}{7 ^{n}}

diverges

Solution steps

n = 0 \sum \infty \frac{n !}{7 ^{n}}

Apply Series Ratio Test:

diverges

= diverges

n = 1 \sum \infty \frac{2 n + 1}{3 ^{n}}

n = 1 \sum \infty n e^{- 9 n}

n = 1 \sum \infty 5^{1 - n}

n = 0 \sum \infty (\frac{3}{10})^{n}

n = 2 \sum \infty (- 0.3)^{n}

What is the sum from n=0 to infinity of (n!)/(7^n) ?
The sum from n=0 to infinity of (n!)/(7^n) is diverges