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

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

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

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

diverges

Solution steps

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

Simplify

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

Apply Series Limit Comparison Test:

diverges

= diverges

n = 2 \sum \infty \frac{n !}{n ^{n}}

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

n = 1 \sum \infty - 2^{n}

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

n = 5 \sum \infty \frac{4 ^{n}}{5 ^{n}}

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