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 principle of mathematical induction :2^(n)<3^(n),n in N

Prove by using the principle of mathemtical induction: 1+2+3+…+n =(n(n+1))/2

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: 1.2+2.2^(2)+3.2^(3)++n.2^(n)=(n-1)2^(n+1)+2

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

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+3.4^(n+2)+5 is divisible by 9

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 using the principle of mathematical induction for all n in Nvdots1+3+3^(2)+...+3^(n-1)=((3^(n)-1))/(2)

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

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