What is the sum from n=1 to infinity}e^{-n of+e^n ?

The sum from n=1 to infinity}e^{-n of+e^n is diverges

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sum from n=1 to infinity}e^{-n of+e^n

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

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

n = 0 \sum \infty \frac{1}{3 - n}

n = 1 \sum \infty \frac{3}{2 n}

k = 1 \sum \infty k e^{- 7 k}

n = 0 \sum \infty 2 (\frac{3}{2})^{n}

What is the sum from n=1 to infinity}e^{-n of+e^n ?
The sum from n=1 to infinity}e^{-n of+e^n is diverges