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

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

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

n = 1 \sum \infty \frac{1}{n ^{e}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{n ^{e}}

Apply p-Series Test:

converges

= converges

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

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

n = 1 \sum \infty \frac{1}{n ^{1.2}}

n = 2 \sum \infty (- 0.15)^{n}

n = 0 \sum \infty \frac{20}{4 ^{n}}

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