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)=11/2
1/3^2<1/(2*3)=1/21/3
1/4^2<1/(3*4)=1/31/4
......................
1/999^2<1/(998*999)=1/9981/999
1/1000^2<1/(999*1000)=1/9991/1000
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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