What is the sum from n=0 to infinity of n 1/(5^n) ?

The sum from n=0 to infinity of n 1/(5^n) is converges

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sum from n=0 to infinity of n 1/(5^n)

n = 0 \sum \infty n \frac{1}{5 ^{n}}

converges

Solution steps

n = 0 \sum \infty n \frac{1}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

\int sec^{2} (3 x t a) n^{5} 3 x d x

y ln (x) \frac{d y}{d x} = (\frac{( y + 1 )}{x})^{2}

(x^{2} - 7)^{2}

\frac{\partial}{\partial x} (ln (cos^{2} (x) + 1))

f (x) = \frac{x}{( 5 x - 4 ) ^{8}}, at x = 1

What is the sum from n=0 to infinity of n 1/(5^n) ?
The sum from n=0 to infinity of n 1/(5^n) is converges