Originally Posted by
Thetheorycase The problem
n
Σi^2 = n(n + 1)(2n + 1)/6
i=1
The base case is correct. Gona get to the meat of the problem
P(k) -------> P(k +1)
1^2 + 2^2 + 3^2 ......+k^2 = k(k +1)(2k+ 1)/6
Now showing k +1
1^2 + 2^2 + 3^2 ......+k^2 + (K +1)^2 = k+1((k +1)+1)((2k+ 1)+1)/6
RHS = (2k^3 + 7k^2 + 10k + 6)/6
LHS =
1^2 + 2^2 + 3^2 ......+k(k +1)(2k+ 1)/6 + (K +1)^2
Before I go on was I right in mulitplyong everything out with k +1 on the RHS so i could math it up with the LHS? in bold
Thank you!!