does it matter where i split the array? i have two different ways but im unsure.

when it comes to induction how did they go from 2^k+1 to 2k

2) Show operation of Moge Sort on Arrey A= 1 is T(n) = n lg n. Base case For n = 21,T(n) = 2 lg 2 = 2.. Suppose n = 2%, 7(n) = n lg n = 2k lg 2k = 2lk. For n = 2k+1 T(n) = 2T (2k+1/2) + 2+1 2T (2k) + 2k+1 2. 2 k + 2k+1 - 2k+1(k +1) = 2k+1 lg 2k+1 = n lg n. By P.M.I.,T(n) = n lg n, when n is an exact power of 2