Subject: Series Derivative
Name: Shamus O'Toole
Question: S(n)=(n(n+1)(2n+1))/6 Hi Shamus,The simplest method is mathematical induction. Let P(n) be the the conjectured identity. Check its validity for n=1. Assume that you have checked it out all the way for n = 1, 2, ..., k1. Now use that assumption to show the validity for n = k. That is assume that 1+4+...+(k1)^{2} = (k1)k(2k1)/6 and then calculate 1+4+..+(k1)^{2}+k^{2} = (k1)k(2k1)/6 + k^{2} and verify that it is (k(k+1)(2k+1))/6. Cheers,Penny
