What is the sum from n=1 to infinity of |n!^2(5^n)| ?

The sum from n=1 to infinity of |n!^2(5^n)| is diverges

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sum from n=1 to infinity of |n!^2(5^n)|

n = 1 \sum \infty n!^{2} (5^{n})

diverges

Solution steps

n = 1 \sum \infty n!^{2} \cdot 5^{n}

Simplify

n!^{2} 5^{n} : 5^{n} n!^{2}

= n = 1 \sum \infty 5^{n} n!^{2}

Apply Series Ratio Test:

diverges

= diverges

\int \frac{1}{2} x^{2} e^{- \frac{1}{2} x} d x

x^{2} e^{- x} + (ln (x))^{2}

\int 3 s h^{3} x d x

\frac{70}{t}

y^{^{'}} = 5 x

What is the sum from n=1 to infinity of |n!^2(5^n)| ?
The sum from n=1 to infinity of |n!^2(5^n)| is diverges