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David G. Stork
David G. Stork
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About the sum of series like $\sum_$\sum\limits_{n=1}^\infty n^{-2}$

I know that $\sum_{n=1}^\infty n^{-2}=\pi^2/6$$\sum\limits_{n=1}^\infty n^{-2}=\pi^2/6$, but shouldn't the sum of rationals be rational? Is this akin to $\sum_{n=1}^\infty n=-1/12$$\sum\limits_{n=1}^\infty n=-1/12$? Or does that mean that, somehow, $\pi^2/6$ is rational?

About the sum of series like $\sum_{n=1}^\infty n^{-2}$

I know that $\sum_{n=1}^\infty n^{-2}=\pi^2/6$, but shouldn't the sum of rationals be rational? Is this akin to $\sum_{n=1}^\infty n=-1/12$? Or does that mean that, somehow, $\pi^2/6$ is rational?

About the sum of series like $\sum\limits_{n=1}^\infty n^{-2}$

I know that $\sum\limits_{n=1}^\infty n^{-2}=\pi^2/6$, but shouldn't the sum of rationals be rational? Is this akin to $\sum\limits_{n=1}^\infty n=-1/12$? Or does that mean that, somehow, $\pi^2/6$ is rational?

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GDGDJKJ
GDGDJKJ
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About the sum of series like $\sum_{n=1}^\infty n^{-2}$

I know that $\sum_{n=1}^\infty n^{-2}=\pi^2/6$, but shouldn't the sum of rationals be rational? Is this akin to $\sum_{n=1}^\infty n=-1/12$? Or does that mean that, somehow, $\pi^2/6$ is rational?