What is the sum from n=0 to infinity of 1/(2+n) ?

The sum from n=0 to infinity of 1/(2+n) is diverges

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sum from n=0 to infinity of 1/(2+n)

n = 0 \sum \infty \frac{1}{2 + n}

diverges

Solution steps

n = 0 \sum \infty \frac{1}{2 + n}

Apply Series Integral Test:

diverges

= diverges

n = 0 \sum \infty \frac{1}{( 1 - n ) ^{3}}

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

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

x = 1 \sum \infty \frac{1}{x ( x + 1 )}

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

What is the sum from n=0 to infinity of 1/(2+n) ?
The sum from n=0 to infinity of 1/(2+n) is diverges