What is the sum from n=0 to infinity of n/((3/2)^n) ?

The sum from n=0 to infinity of n/((3/2)^n) is converges

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sum from n=0 to infinity of n/((3/2)^n)

n = 0 \sum \infty \frac{n}{( \frac{3}{2} ) ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n}{( \frac{3}{2} ) ^{n}}

Apply Series Ratio Test:

converges

= converges

\frac{( s + 1 ) ^{3}}{s ^{4}}

\int t d t

\int 3^{4 x} d x

\int (\frac{sin ( 2 x )}{sin ( x )}) d x

3 - 2 e^{x}

What is the sum from n=0 to infinity of n/((3/2)^n) ?
The sum from n=0 to infinity of n/((3/2)^n) is converges