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What does the following sequence converge to: Sum[1/n^8, from n=1 to infinity]?. Any help would be appreciated. Thank you.

Guest Jun 6, 2017

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Sum[1/n^8, from n=1 to infinity]

 

The sum of the reciprocals of all counting numbers to the EVEN powers, namely: 1/n^2, 1/n^4, 1/n^6....., all the way up to 1/n^26 and beyond, was proven by Leonhard Euler to converge to the same powers of Pi divided by some constant. In this particular case, it converges to =Pi^8 / 9,450 exactly.

Guest Jun 6, 2017
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 #1
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Best Answer

Sum[1/n^8, from n=1 to infinity]

 

The sum of the reciprocals of all counting numbers to the EVEN powers, namely: 1/n^2, 1/n^4, 1/n^6....., all the way up to 1/n^26 and beyond, was proven by Leonhard Euler to converge to the same powers of Pi divided by some constant. In this particular case, it converges to =Pi^8 / 9,450 exactly.

Guest Jun 6, 2017

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