Posted by George on .
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,
1 * 1 = 1
1/3 * 1/3 = 1/9
1/1000 * 1/1000 = 1/1,000,000 
MATHS 
bobpursley,
Here are three proofs, take your pick.
http://en.wikipedia.org/wiki/Basel_problem 
MATHS 
Anonymous,
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,
http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/NYU%20Basel%20Problem%20Paper.PDF

MATHS 
Alexander,
Could you expand more on the answer anoymomous?