What is the sum from n=0 to infinity of n(6/7)^n ?

The sum from n=0 to infinity of n(6/7)^n is converges

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sum from n=0 to infinity of n(6/7)^n

n = 0 \sum \infty n (\frac{6}{7})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{6}{7})^{n}

Apply Series Ratio Test:

converges

= converges

f (x) = x^{3} + 2

\frac{d}{d x} (x - 10)

t an g e n t y = 6 e^{x} cos (x), (0, 6)

\frac{d}{d x} (3 ln (x^{2}))

t an g e n t e^{x}, at x = 5

What is the sum from n=0 to infinity of n(6/7)^n ?
The sum from n=0 to infinity of n(6/7)^n is converges