Prove by the principle of mathematical induction, that
`3xx6+6xx9+9xx12+....+(3n)xx(3n+3)=3n(n+1)(n+2)`

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by the principle of mathematical induction that for all n in N : 1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)

Prove the following by the principle of mathematical induction: \ 1. 2+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/3

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .

Using the principle of mathematical induction, prove that 1.2+2.3+3.4+......+n(n+1)=(1)/(3)n(n+1)(n+2)

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+(3xx4^(n+2))+5 is divisible by 9 .

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

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 the principle of mathematical induction that for all n belongs to N :\ 1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)

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