Recall the master theorem as stated in class. we are interested in recurrences of the form.

t$($n$)=$ aT$($n$/$b$)+$ f$($n$)$

Define Kn $=$ af$($n$/$b$)/$f$($n$)$ and let k:$=$ lim kn$.$ In order to simplify the theorem and its proff, we will further assume that tehre is some n$0$ such that n$>=$ n$0$

a$)$ Write out the first few terms in the recursive expansion of T$($n$).$ sjow that we can reqrite the $-$th term