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

Prove by using the principle of mathemtical induction: 1^3+3^3+5^3+…+(2n-1)^3 =n^2 (2n^2-1)

Prove by using the principle of mathemtical induction: If u_0=2, u_1 = 3 and u_(n+1)=3u_n -2u_(n-1), show that u_n = 2^n +1, n epsilon N

Prove the following by using the principle of mathematical induction for all n in N 1.2+2.2^2 + 3.2^3 + ……….+ n.2^n =(n-1) 2^(n+1) + 2

Prove that by using the principle of mathematical induction for all n in N : 1+ 3+ 3^(2)+ …. + 3^(n-1)= ((3^(n)-1))/(2)

Prove that by using the principle of mathematical induction for all n in N : 1+ 3+ 3^(2)+ …. + 3^(n-1)= ((3^(n)-1))/(2)

Prove the following by using the principle of mathematical induction for all n in N 1+3+3^2 +…………+3^(n-1) = (3^n -1)/(2)

Prove the following by using the principle of mathematical induction for all n in N :- 1 +3 + 3^2 +....+3^(n-1)=((3^n-1))/2 .

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 for all n in N 1.3+2.3^2+3.3^3 + ……….+n.3^n = ((2n-1)3^(n+1) + 3)/(4)