Prove each of the following statements using strong inductio

Prove each of the following statements using strong induction.

B AND C

Define the sequence {h_n} as follows: h_0 = 5/3 h_1 = 11/3 h_n = 3h_n-1 + 4h_n-2 + 6n, for n greaterthanorequalto 2 Prove that for n greaterthanorequalto 0, h_n = 2 middot 4^n + 3/2 (-1)^n - n - 11/6 Define the sequence {g_n} as follows: g_0 = 51 g_1 = 348 9_n = 5g_n-1 - 6g_n-2 + 20 middot 7^n for n greaterthanorequalto 2 Prove that for n greaterthanorequalto 0, g_n = 2^n + 3^n + 7^n + 2.

Solution

when h=0

h₀₌2.4⁰+3/2(-1)⁰-0-11/6

=2.1+3/2(1)-11/6   (x⁰ =1)

=2+3/2-11/6

(12+9-11)/6

=(21-11)/6

=10/6

=5/3

hence proved for h₀

h₁=2.4-3/2-1-11/6

=8-3/2-1-11/6

=(48-9-6-11)/6

=(48-26)/6

=22/6=11/3 proved for h₁

_(C).

g₀=2⁰+3⁰+7⁰⁺²

=1+1+7⁰.7²

=2+49=51 proved for g₀

g₁=2¹+3¹+7¹⁺²

=2+3+7*7*7

=5+49*7

5+343=348 proved for g_1.