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

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

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

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

diverges

Solution steps

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

Apply Series Integral Test:

diverges

= diverges

k = 3 \sum \infty \frac{1}{4 k ^{2} - 1}

k = 1 \sum \infty \frac{1}{k} - \frac{1}{k + 1}

n = 2 \sum \infty \frac{n !}{( 2 n ) !}

n = 1 \sum \infty \frac{1}{n ^{3} + n}

n = 1 \sum \infty \frac{1}{n ^{3} + 8}

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