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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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