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

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

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

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

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