example of how work should be done:

1. (15 pts) For the following recurrence, T(n) = 0 n = 1 T(n) = 4T(n-1) + c n>1 b. Use the substitution method to prove your above solution is correct. Show your work in sufficient details. Given the recurrence: T(n) = c n = 1, 2 T(n) = 3T(n/3) en n>2 Use the substitution method to show T(n)-(nlgn). Show your work in sufficient details. nzz Tinac I nr 1,2 Induction T(n) = 31 C4) ton Show + (n) c'ntagin let-c'nten so c'ac 30' 1/3 log (%) + in c'n logn - c'nt en c'2c, nazl base Case : Combine two Steps let c'226 223 This c'n logan given legno Ten) Scholten Igan n= tn=( 2 'n legn Is cold no Try n=3 T(n) = 0 Enign) T(3) = 3 TC1) tch 30 30 6 c'3 lage3 6C = 30 20 = c