okay, it's not exactly what I was looking for but I understand now what you were implying. Thank you for the help.
kp wrote: > He proved by induction that > 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 - 1/n > which implies > 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 for all n >=2 > > I think that is the utmost perfect solution you are looking for. > > <firstname.lastname@example.org> wrote in message > news:email@example.com... > > Hi Torsten, thank you for your reply however you're solving a different > > problem here. It appears that you've introduced a -1/n to the right of > > the inequality for your convinience. That isn't the orignial problem. > > I'm not sure what you're doing at all. Please everyone, here's the > > problem ((((( 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 ))))) FOR ALL n, > > greater than or equal to 2, PROOF by INDUCTION. I only capitalized for > > clarity, not yelling here. > > > > Torsten Hennig wrote: > >> >Prove by induction that 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 >Please help! > >> >Thank you! > >> > >> Hi, > >> > >> show by induction that > >> 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 - 1/n > >> In the induction step, use that > >> 1/(n+1)^2 < 1/(n*(n+1)) = 1/n - 1/(n+1) . > >> > >> Best wishes > >> Torsten. > >