# Choosing Constant for Last Step in Substitution METHOD $T(n)= 5T(n/4) + n^2$

I figured out a solution to a recurrence relation, but I’m not sure what the constant should be for the last step to hold.

$$T(n)= 5T(n/4) + n^2$$

Guess: $$T(n) = O(n^2)$$

Prove: $$T(n) \leq cn^2$$

Breakdown

$$T(n) \leq 5(c(n/4)^2) + n^2$$

$$= (5/16)cn^2 + n^2$$

$$\leq cn^2$$

For the last step to hold I’m not sure what the value of c should be because of the (5/16). My guess would be c >= 1 and I’m not sure if that would hold.