Prove the following by using iduction for all `n in N`. `1+2+3+.....+n=(n(n+1))/(2)`

Prove the following by using induction for all n in N . 1+2+3+.....+n=(n(n+1))/(2)

Prove the following by using induction for all n in N . 1+2+3+.....+n=(n(n+1))/(2)

Prove the following by the method of induction for all n in N : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)

Prove the following by the method of induction for all n in N : 1^2 + 3^2 + 5^2 + ... + (2n - 1)^2 = n/3 (2n -1) (2n +1)

Prove the following by the method of induction for all n in N : 3 + 7+ 11 +.. to n terms = n(2n + 1).

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

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)

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 1^2 +3 ^2 + 5^2 +………..+ (2n-1)^2 = (n(2n - 1)(2n+1))/(3)

Prove the following by using the principle of mathematical induction for all n in N 1.2+2.3+3.4+…….+n.(n+1) = [ (n(n+1)(n+2))/(3)]