What is the sum from n=2 to infinity of ((n+1)/n)^n ?

The sum from n=2 to infinity of ((n+1)/n)^n is diverges

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sum from n=2 to infinity of ((n+1)/n)^n

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

diverges

Solution steps

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

(\frac{n + 1}{n}) = (\frac{n}{n} + \frac{1}{n})

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

Simplify

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

Apply Series Divergence Test:

diverges

= diverges

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What is the sum from n=2 to infinity of ((n+1)/n)^n ?
The sum from n=2 to infinity of ((n+1)/n)^n is diverges