What is the sum from n=0 to infinity of n^3*5^{-n} ?

The sum from n=0 to infinity of n^3*5^{-n} is converges

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sum from n=0 to infinity of n^3*5^{-n}

n = 0 \sum \infty n^{3} \cdot 5^{- n}

converges

Solution steps

n = 0 \sum \infty n^{3} \cdot 5^{- n}

Apply Series Ratio Test:

converges

= converges

x \to 0 lim (\frac{e ^{3 x} - 1}{sin ( 2 x )})

y^{^{'}} = x (4 - y)

\int (2 x + 5) e^{- x} d x

\int tan (x) sin^{2} (x) d x

x^{2}, x + 2, - 1, 2

What is the sum from n=0 to infinity of n^3*5^{-n} ?
The sum from n=0 to infinity of n^3*5^{-n} is converges