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

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

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

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

diverges

Solution steps

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

\frac{1}{n + 1} = \frac{n + 2}{n + 1} - 1

= n = 1 \sum \infty 1 + \frac{n + 2}{n + 1} - 1

Simplify

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

Apply Series Divergence Test:

diverges

= diverges

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