What is the sum from n=3 to infinity of n^2e^{-n^3} ?

The sum from n=3 to infinity of n^2e^{-n^3} is converges

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sum from n=3 to infinity of n^2e^{-n^3}

n = 3 \sum \infty n^{2} e^{- n^{3}}

converges

Solution steps

n = 3 \sum \infty n^{2} e^{- n^{3}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{n + 1}{n 2 ^{n}}

n = 1 \sum \infty \frac{n !}{7 ^{n}}

n = 1 \sum \infty \frac{1}{( 3 n - 1 ) ^{2}}

k = 1 \sum \infty k

n = 0 \sum \infty \frac{n}{1 + 2 n}

What is the sum from n=3 to infinity of n^2e^{-n^3} ?
The sum from n=3 to infinity of n^2e^{-n^3} is converges