MHB What are the next steps after finding a pattern in iterative substitution?

[fvnn]

Hi i Have this equation:
[M]T(n)=2T(n/2)+n^2[/M]


I understand for iterative substitution you need to find patterns so here's what i got:
[M]2^2T(n/2^2)+n2/2+n^2
2^3T(n/2^3)+n2/2^2+n2/2+n^2[/M]

My question is what to do after you have found the pattern?

 

[Evgeny.Makarov]

My question is what to do after you have found the pattern?

Whatever the problem tells you. You could write the general form of the pattern (after applying the definition of $T$ $n$ times). You could write the explicit formula for $T$ when $n$ is a power of 2 for a given $T(1)$ and then prove it by induction.