What is the sum from n=1 to infinity}e^{8/n of*1/n ?

The sum from n=1 to infinity}e^{8/n of*1/n is converges

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sum from n=1 to infinity}e^{8/n of*1/n

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

converges

Solution steps

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

\frac{8}{n} = \frac{8 - n}{n} + 1

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

Simplify

e^{\frac{8 - n}{n} + 1} \frac{1}{n} : \frac{e ^{\frac{8}{n}}}{n}

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

Apply Series Integral Test:

converges

= converges

3 \frac{d ^{2} y}{d x ^{2}} - 21 \frac{d y}{d x} + 36 y = 5 sin (3 x)

d er i v a t i v e \frac{1}{x ^{3}}

\frac{\partial}{\partial y} (2 x y^{2} + 3 x^{2})

d er i v a t i v e f (x) = 8^{x}

d er i v a t i v e (2 x - 3)^{3} (x^{4} + 1)^{2}

What is the sum from n=1 to infinity}e^{8/n of*1/n ?
The sum from n=1 to infinity}e^{8/n of*1/n is converges