[1.3+2.4+3.5+.....+n(n+2)],[qquad =(1)/(6)n(n+1)(2n+7)]

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)

1.3 + 2.4 + 3.5 + …… + n(n+2) =( n(n+1)(2n+7))/6

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 3.5 + 5.7 +...+ (2n-1)(2n+1)=(n(4n^2 +6n-1))/3

1.2.3+2.3.4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

By the Principle of Mathematical Induction, prove the following 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 : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)