can you please explain this a bit. I understand the first parts and the calculations and everything. My issue stems at the end where it says "until..." because I don't understand how they got that conclusion. And the parts after the until are very confusing

General Divide-and-Conquer Recurrence Recurrence relation: T(n) = aT(n/b) +f(n) where f(n) E O(no), d20 Solve by backward substitution: T(n) = aT(n/b) + f(n) = a(aT(n/b/b)+f(n/b)) +f(n) = a?T(n/b2) + af(n/b) + f(n) = a2(T(n/b2/b) + f(n/b2)) + af(n/b) +f(n) = a T(n/b3)+ a-f(n/b2) + af(n/b) +f(n) ...... = akT(n/bk) + ak-if(n/bk-1) + ak-2f(n/bk-2) + ...+ af(n/b) + f(n) until n/bk = 1, k = login, and assume f(n) = nd = alogg" + nd((a/bd)k-14(a/bd)k-2+ ... + (a/bd) + 1) = nlogba + n'((a/bd)k - 1)/((a/bd) - 1) 5