What is the sum from n=0 to infinity of e^{(-n^6)/8} ?

The sum from n=0 to infinity of e^{(-n^6)/8} is converges

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sum from n=0 to infinity of e^{(-n^6)/8}

n = 0 \sum \infty e^{\frac{- n ^{6}}{8}}

converges

Solution steps

n = 0 \sum \infty e^{\frac{- n ^{6}}{8}}

Apply Series Root Test:

converges

= converges

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

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

n = 1 \sum \infty 60 (0.1)^{n}

n = 0 \sum \infty (\frac{5}{9})^{n}

n = 1 \sum \infty \frac{n !}{9 4 ^{n}}

What is the sum from n=0 to infinity of e^{(-n^6)/8} ?
The sum from n=0 to infinity of e^{(-n^6)/8} is converges