How to solve the following recurrence? $T(n) = 4T(\frac{n}{2})+n!$ Hello all I am kinda confused on how to solve the above recurrence since the masters theorem would not work with the above equation. Could anyone please help me solving this and showing me the steps? Requirement is to find asymptotically tightest bound.

$$T(n) = 4T(\frac{n}{2})+n!$$
"... the masters theorem would not work with the above equation" is not right. From the master theorem, as we know $n! = \Omega(n^3)$, and $4\left(\frac{n}{2}\right)! &lt; 0.9 n!$ ($k = 0.9$) for large enough $n$, so $T(n) = \Theta(n!)$.

To know more about this case, follow this link and find third case of the master theorem.