Prove by using the principle of mathemtical induction: ` 3.2^2 +3^2.2^

1.	Prove by using the principle of mathemtical induction: ` 3.2^2 +3^2.2^3+…+3^n .2^(n+1) = 12/5 (6^n-1) `
Answer» `P(k): 32^(2)+3^(2)2^(3)+…+3^(k)2^(k+1)=12/5 (6^(k)-1)`. Now, ` (32^(2)+3^(2)3^(2)+…+3^(k)2^(k+1))+3^(k+1)2^(k+2)` ` ={12/5(6^(k)-1)+3^(k+1)2^(k+1)2}=1/5{12(6^(k)-1)+10xx6^(k+1)}` ` = 1/5 *{2(6^(k+1)-6)+10 xx 6^(k+1)} = 12/5 (6^(k+1)-1)`.

Discussion