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

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

Prove the following by the principle of mathematical induction: 1.3+2.4+3.5++(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

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. 2+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/3

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: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: 1.2+2.3+3.4++n(n+1)=(n(n+1)(n+2))/(3)

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=(1)/(2)n(3n+1)