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

\int 2000 (x - 4) e^{x^{2} - 8 x} d x

2 x^{2} - 4

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

n = 1 \sum \infty 1 7^{n} x^{n} n!

\frac{d y}{d x} = 3 x^{2} (y^{2} + 1)

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