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

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

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

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

diverges

Solution steps

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

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

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

Simplify

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

Apply Series Divergence Test:

diverges

= diverges

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