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: 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: 1.3+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)/(3)n(4n^(2)-1)

Prove the following by using the Principle of mathematical induction AA n in N 3^(n)>2^(n)

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

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 using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

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+2+3++n=(n(n+1))/(2)ie,the sum o the first n natural numbers is (n(n+1))/(2)