What is the sum from n=1 to infinity of (n!)/(n5^n) ?

The sum from n=1 to infinity of (n!)/(n5^n) is diverges

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sum from n=1 to infinity of (n!)/(n5^n)

n = 1 \sum \infty \frac{n !}{n 5 ^{n}}

diverges

Solution steps

n = 1 \sum \infty \frac{n !}{n \cdot 5 ^{n}}

Apply Series Ratio Test:

diverges

= diverges

x \to 0 lim (\frac{4 ^{x} - 1}{x})

(\frac{3 x ^{2}}{2 x + 4})^{3}

2 x y^{^{'}} + y = 6 x, y (4) = 25

y = - 2 x^{3}, (1, - 2)

f (x) = 6 tan (x), at x = \frac{π}{6}

What is the sum from n=1 to infinity of (n!)/(n5^n) ?
The sum from n=1 to infinity of (n!)/(n5^n) is diverges