What is the sum from n=0 to infinity of 1/(e^{5n)} ?

The sum from n=0 to infinity of 1/(e^{5n)} is converges

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sum from n=0 to infinity of 1/(e^{5n)}

n = 0 \sum \infty \frac{1}{e ^{5 n}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{e ^{5 n}}

Apply Series Ratio Test:

converges

= converges

\int (- 4 x^{3} + 2 e^{- 2 x} + \frac{1}{2 x}) d x

\frac{d y}{d x} + 4 (tan (4 x)) y = 10 cos (4 x)

x \to 0 lim (\frac{x}{( 4 ^{x} - 2 ^{x} )})

\frac{d}{d x} (arcsin (2 x^{5}))

x^{2} + 9

What is the sum from n=0 to infinity of 1/(e^{5n)} ?
The sum from n=0 to infinity of 1/(e^{5n)} is converges