How come we are assuming n = 2^k and k =logn here, also how come we are ignoring cn/4+cn/2 and justifying it as cn

T(n) 2T(n/2)cn = 2(2T(n/4) + cn/2) + cn - 2(2(2T(n/8) cn/4) + cn/2)cn k timeS = n T(1) + cn lgn -O(nlogn)