The seq of real numbers u1, u2, u3... is such that
u(r+1) = u(r)/(1-r^2.u(r))
Using method of differences, show that
1/u1 - 1/u(N) = 1/6 (N-1)N(2N-1)
To Prove It,
Sorry if i gave the impression i didn't even try, but seriously the community's really great here and i'm looking forward to help others out in future..
I tried my hand at it but only got into summation of recurrence terms- and though using method of differences pretty cuts it down alot, i just can't show the result. i do know that sum to n of r^2 is 1/6n(n+1)(2n+1).