What is the sum from n=1 to infinity}(e^{6/n of)/n ?

The sum from n=1 to infinity}(e^{6/n of)/n is converges

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sum from n=1 to infinity}(e^{6/n of)/n

n = 1 \sum \infty \frac{e ^{\frac{6}{n}}}{n}

converges

Solution steps

n = 1 \sum \infty \frac{e ^{\frac{6}{n}}}{n}

Apply Series Integral Test:

converges

= converges

n = 1 \sum \infty \frac{2}{n ^{2} + 4}

n = 1 \sum \infty \frac{1}{n ( n + 4 )}

n = 1 \sum \infty \frac{e ^{n}}{n ^{8}}

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

n = 0 \sum \infty \frac{n + 1}{3 ^{n}}

What is the sum from n=1 to infinity}(e^{6/n of)/n ?
The sum from n=1 to infinity}(e^{6/n of)/n is converges