HELP WITH RECURRENCE RELATIONS PROBLEM PLEASE!!?

T(0) = 1 = (5/2)^0
So, it is true for n = 0

Suppose it ir true for n = k , where k > 0
That is, T(k) ≤ (5/2)^k

When n = k+1 ,
T(k+1)
= 2*T(k) + T(k-1)
≤ 2*(5/2)^k + (5/2)^(k-1)
= (5/2)^(k-1) * ( 2*5/2 + 1 )
= (5/2)^(k-1) * 6
< (5/2)^(k-1) * (25/4)
= (5/2)^(k+1)
Hence, it is true for n = k+1

By the mathematical induction, it is true for all non-negative integer n

Q.E.D.