The function f : {1, 2, 3, . . .} R is defined by f(1) = 2, f(n) = 1 2 f(n 1) + 1 f(n1) if n 2. Prove that for every integer n 1, f(n) = 3 2 n1 + 1 3 2n1 1 . Note that 3 2^n1 is 3 to the power of 2n1

Question 2: The function f :1,2,3,...) -R is defined by if n > 2. Prove that for every integer n 21, 32-1 +1 32 1 Note that 32" is 3 to the power of 21