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: 3.2^2 +3 . 2^3+…+3^n .2^(n+1) = 12/5 (6^n-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+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

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. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+(3xx4^(n+2))+5 is divisible by 9 .

Prove the following by the principle of mathematical induction: \ 7^(2n)+2^(3n-3). 3^(n-1) is divisible 25 for all n in Ndot

Prove the following by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

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