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What is the resulting sum of this expression and why?
∑[1/n^10, n=1 to 10,000] - [pi^10/93,555]=? Appreciate any help. Thanks.

 Jun 5, 2017
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You are right! It is a beautiful result. Do you know why? Because:

 

The sum of: 1/n^10 from n=1 to infinity =Pi^10 / 93,555 exactly! This was proven by the great Swiss mathematician Leonhard P. Euler almost 250 years. So that your expression of:

 

∑[1/n^10, n=1 to 10,000] - [pi^10/93,555]=0, or nearly so, because the first sum goes from 1 to infinity, while yours is only summed up to 10,000 terms.

 Jun 5, 2017

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