Deriving Summation Formulas for the Sum of Consecutive Powers - Part 4 (k ≥ 3)

Course Web Page: sites.google.com/view/slcmath...
Summation Formula - Approach 1: drive.google.com/file/d/12grS...
Summation Formula - Approach 2: drive.google.com/file/d/12iI2...
Deep Dive - Approach 1: drive.google.com/file/d/12nK6...
Deep Dive - Approach 2: drive.google.com/file/d/12mnr...

[@errorhostnotfound1165]

I know that he said that finding the generic formula for i^k is supposed to be an exercise, but I have gotten stuck at (n+1)sum((2i-1)^(k/2)) - sum(i(2i-1)^(k/2)), so what is it? I haven't been able to find anything online so far

[@slcmathpc]

The idea that I have presented in these videos only allows one to find the summation formula for i^k recursively, so you can find that of i^3, then i^4, then i^5, and so on, but you cannot jump to say i^20, without first finding the formula for all of the powers lower than 20. Hope this clarifies things. :-)