I spent 3 days on trying to solve this question.

Someone please solve and proof it by induction.

It is the first time I am dealing with a recursion relation that involves logs.

Please solve and proof it for me so that I can understand what I’ve been doing wrong.

It needs to be solved through iterative substitution method.

Edit:

So final answer is n^2*log*log(n);

but then how do you Proof it by induction…

how will you prove the original equation confirms to P(k+1), i.e.

(k+1)^2*log*log(k+1)