Posted by **George** on Saturday, July 9, 2011 at 10:49pm.

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.

- MATHS -
**Ms. Sue**, Saturday, July 9, 2011 at 10:51pm
1 * 1 = 1

1/3 * 1/3 = 1/9

1/1000 * 1/1000 = 1/1,000,000

- MATHS -
**bobpursley**, Saturday, July 9, 2011 at 10:58pm
Here are three proofs, take your pick.

http://en.wikipedia.org/wiki/Basel_problem

- MATHS -
**Anonymous**, Saturday, July 9, 2011 at 11:07pm
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

- MATHS -
**bobpursley**, Saturday, July 9, 2011 at 11:10pm
http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/NYU%20Basel%20Problem%20Paper.PDF

- MATHS -
**Alexander**, Sunday, July 10, 2011 at 7:56am
Could you expand more on the answer anoymomous?

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