1 * 1 = 1
1/3 * 1/3 = 1/9
1/1000 * 1/1000 = 1/1,000,000
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.
5 answers
Here are three proofs, take your pick.
http://en.wikipedia.org/wiki/Basel_problem
http://en.wikipedia.org/wiki/Basel_problem
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
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
http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/NYU%20Basel%20Problem%20Paper.PDF
Could you expand more on the answer anoymomous?