Prove by using the principle of mathemtical induction: ` 3.2^2 +3 . 2^3+…+3^n .2^(n+1) = 12/5 (6^n-1) `

Prove by using the principle of mathemtical induction: 1^3+3^3+5^3+…+(2n-1)^3 =n^2 (2n^2-1)

Prove by using the principle of mathemtical induction: If u_0=2, u_1 = 3 and u_(n+1)=3u_n -2u_(n-1), show that u_n = 2^n +1, n epsilon N

Prove the following by the principle of mathematical induction: \ 1. 2+2. 2^2+3. 2^3++n .2^n=(n-1)2^(n+1)+2

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: \ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6