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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

n = 2 \sum \infty (1 + \frac{1}{3})^{- n}

n = 0 \sum \infty sin (\frac{nπ}{2})

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

n = 0 \sum \infty \frac{1}{100 + n}

n = 1 \sum \infty \frac{7}{n ( n + 2 )}

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