What is the sum from n=1 to infinity of (4n+2)/(5^n) ?

The sum from n=1 to infinity of (4n+2)/(5^n) is converges

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sum from n=1 to infinity of (4n+2)/(5^n)

n = 1 \sum \infty \frac{4 n + 2}{5 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{4 n + 2}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

\int x (x + 1)^{2} d x

\frac{d y}{d x} + \frac{1}{x + 1} y = x^{- 2}

\int \frac{1}{x x ^{2} + 16} d x

\int 4 x e^{3 x} d x

e^{x} + e^{- x}

What is the sum from n=1 to infinity of (4n+2)/(5^n) ?
The sum from n=1 to infinity of (4n+2)/(5^n) is converges