`1+4+10+19+.........+(3n^2-3n+2)/2=`

Prove, by method of induction, for all n in N : 1^2 + 4^2 + 7^2 +...+ (3n - 2)^2 = n/2 (6n^2 - 3n - 1)

Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

By the Principle of Mathematical Induction, prove the following for all n in N : 1+4+7+.....+ (3n-2)= (n(3n-1))/2 .

Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+.......+1/((3n-2)(3n+1))=n/(3n+1) for all n in N

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

1.3+2.3^(2)+3.3^(3)+............+n.3^(n)=((2n-1)3^(n+1)+3 )/(4)

For all nge1 , prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

Prove the following by using the principle of mathematical induction for all n in N 1.2.3.+2.3.4+….+n(n+1)(n+2) = (n(n+1)(n+2)(n+3) )/(4)