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

The sum from n=0 to infinity of (1+5/n)^n is diverges

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sum from n=0 to infinity of (1+5/n)^n

n = 0 \sum \infty (1 + \frac{5}{n})^{n}

diverges

Solution steps

n = 1 \sum \infty (1 + \frac{5}{n})^{n}

Apply Series Divergence Test:

diverges

= diverges

n = 0 \sum \infty (\frac{1}{22})^{n}

n = 0 \sum \infty 5 (\frac{9}{10})^{n}

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

n = 2 \sum \infty \frac{n ^{4}}{n ^{3}}

n = 2 \sum \infty n e^{- 5 n}

What is the sum from n=0 to infinity of (1+5/n)^n ?
The sum from n=0 to infinity of (1+5/n)^n is diverges