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: \ 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. 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+2^2+3^2++n^2=(n(n+1)(2n+1))/6

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: (1-1/(2^2))(1-1/(3^2))(1-1/(4^2))------(1-1/(n^2))=(n+1)/(2n) for all natural numbers \ ngeq2.

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: \ x^(2n-1)+y^(2n-1) is divisible by x+y for all n in NNdot

Prove the following by the principle of mathematical induction: 1+2+3++n=(n(n+1))/2idote , the sum o the first n natural numbers is (n(n+1))/2dot