+0  
 
+1
89
1
avatar

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.

Guest Jun 5, 2017
Sort: 

1+0 Answers

 #1
avatar
+1

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.

Guest Jun 5, 2017

11 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details