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.
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
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
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
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?