Reducing Algorithm Time Complexity of Recursive Function

Question

This is the code for function f(T,k) where

f(T,k)=∑(from i=1 to i≤len(T)) T[i], for k=0, where len(T) is length of array T.
f(T,k)=∑(from i=1 to i≤len(T)) ∑(f