What is the sum from n=0 to infinity of n(1/3)^n ?

The sum from n=0 to infinity of n(1/3)^n is converges

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sum from n=0 to infinity of n(1/3)^n

n = 0 \sum \infty n (\frac{1}{3})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{1}{3})^{n}

Apply Series Root Test:

converges

= converges

x \to 0 lim (cos (\frac{4}{x}))

(- \frac{3}{4}, \frac{1}{4}), (\frac{1}{2}, - \frac{3}{2})

f (x) = x^{2} - 4, g (x) = 0, x = - 4, x = 3

\frac{\partial}{\partial x} (2 x - cos (y))

What is the sum from n=0 to infinity of n(1/3)^n ?
The sum from n=0 to infinity of n(1/3)^n is converges