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

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

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

k = 0 \sum \infty \frac{k}{3 ^{k}}

converges

Solution steps

k = 0 \sum \infty \frac{k}{3 ^{k}}

Apply Series Ratio Test:

converges

= converges

1 \cdot sin (x) + x \cdot cos (x)

sin (5 x) y^{^{'}} = 0

f (x) = 7 x + 10 x

f^{^{''}} (x) = 2, f^{^{'}} (2) = 5, f (3) = 2

\frac{\partial}{\partial x} (36 x^{8} y^{5} + 8 x^{7} y^{3})

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