a) Prove the following statement by using induction method. n(n-1)(n+1) 3 n-1 For any integer n...

 

Transcribed Image Text:

a) Prove the following statement by using induction method. n(n-1)(n+1) 3 n-1 For any integer n ≥ 2, E10+1) = (7 Marks) b) Let bo, b₁ b₂,... Be the sequence defined by the explicit formula bo = A 2" + B for each integer n > 0, where A and B are real number. i. Show that for any choice of A and B, bk=3bk-1-2bk-2 for every integer k≥ 2. ii. (4 Marks) Find the value of A and B for bk = 3bk-1-2bk-2 k ≥ 2 with initial conditions bo = 1 and b₁ = 3. c) Let M = {K € N: 4 ≤ k < 12) and N = {k E N: k = 2n}. i. Find Mn N Find M\N ii. (5 Marks) (4 Marks) a) Prove the following statement by using induction method. n(n-1)(n+1) 3 n-1 For any integer n ≥ 2, E10+1) = (7 Marks) b) Let bo, b₁ b₂,... Be the sequence defined by the explicit formula bo = A 2" + B for each integer n > 0, where A and B are real number. i. Show that for any choice of A and B, bk=3bk-1-2bk-2 for every integer k≥ 2. ii. (4 Marks) Find the value of A and B for bk = 3bk-1-2bk-2 k ≥ 2 with initial conditions bo = 1 and b₁ = 3. c) Let M = {K € N: 4 ≤ k < 12) and N = {k E N: k = 2n}. i. Find Mn N Find M\N ii. (5 Marks) (4 Marks)