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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int cos^{2} (x) \cdot sin (2 x) d x

\int \frac{- x - 1}{2 ( x ^{2} + 1 )} d x

\int 20 cot^{4} (x) d x

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

y^{^{''}} - 11 y^{^{'}} + 30 y = 20 e^{t}

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