Asked by George

Prove that
one over one squared plus one over two squared plus one over three squared....... plus one over 1000 squared is smaller than two. Details please.

Answers

Answered by Ms. Sue
1 * 1 = 1
1/3 * 1/3 = 1/9
1/1000 * 1/1000 = 1/1,000,000

Answered by bobpursley
Here are three proofs, take your pick.

http://en.wikipedia.org/wiki/Basel_problem
Answered by Anonymous
1/2^2<1/(1*2)=1-1/2
1/3^2<1/(2*3)=1/2-1/3
1/4^2<1/(3*4)=1/3-1/4
......................
1/999^2<1/(998*999)=1/998-1/999
1/1000^2<1/(999*1000)=1/999-1/1000

Now add all inequalities
Answered by bobpursley
http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/NYU%20Basel%20Problem%20Paper.PDF
Answered by Alexander
Could you expand more on the answer anoymomous?

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