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Reciprocal Sums

Calculus Level 1

It is known that $\frac{ 1}{1} + \frac{1}{2} + \frac{1}{3} + \cdots$ is infinite.

What about

$\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots \ ?$

Hint:

It is finite and less than 2 It is finite and equals 2 It is finite and greater than 2 It is infinite

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by Calvin Lin

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