Complete and correct answer in order to give full creditthan

Complete and correct answer in order to give full credit,thank you:

Solve the following recurrence equations, expressing the answer in Big-Oh notation. Assume that T(n) is constant for sufficiently small n.

(e) T(n) = T(n 1) + log n

(f) T(n) = T(n 3) + n

Solution

(a)  T(n) = T(n 1) + log n

T(n) = T(n-2) + log(n-1) + log(n)

T(n) = T(n-3) + log(n-2) + log(n-1) + log(n)

...

T(n) = T(0) + log(1) + log(2)....log(n)

assume T(0) =0

T(n) = log(1.2.3.....n) (loga+ logb = log a.b)

T(n) = log(n!).

(f) T(n) = T(n-3) + n

T(n) = T(n-6) + n-3 + n

T(n) = T(n-9) + n-6 + n-3 + n

...

T(n) = T(0) + 3 + 6+ ...n-3 + n

T(n) = 0 + 3+ 6...n

T(n) = 3(1+2...n/3)

T(n) = 3* (n/3*(n/3+1)/2)

T(n) = O(n²)