What is the sum from n=2 to infinity of (n-2)/(n5^n) ?

The sum from n=2 to infinity of (n-2)/(n5^n) is converges

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sum from n=2 to infinity of (n-2)/(n5^n)

n = 2 \sum \infty \frac{n - 2}{n 5 ^{n}}

converges

Solution steps

n = 2 \sum \infty \frac{n - 2}{n \cdot 5 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 3 \sum \infty \frac{7 ^{n}}{1 4 ^{n}}

x \to \infty lim (2 + \frac{5}{x})

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

\frac{d}{d x} (ln (\frac{1 - x}{1 + x}))

x \to 0 lim ((1 + 5 x)^{\frac{6}{x}})

What is the sum from n=2 to infinity of (n-2)/(n5^n) ?
The sum from n=2 to infinity of (n-2)/(n5^n) is converges