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

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

d er i v a t i v e (x^{2} - 7)^{2}

t an g e n t f (x) = \frac{x}{( 5 x - 4 ) ^{8}}, at x = 1

s l o p e (- 2.2) (5.3)

t an g e n t y = x (x + 1)^{5}, (1, 32)

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