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

For all nge1 , prove that 1/1.2+1/2.3+1/3.4+..........+1/(n(n+1))=n/(n+1)

For all nge1 , prove that 1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n/(2n+1)

Using mathematical induction prove that 1/(1.2.3)+1/(2.3.4)+......+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2)) for all n in N .

For all nge1 , prove that 1^2+2^2+3^2+……….+n^2gtn^3/3

For all nge1 ,prove that 1+2+3+……+nlt1/8(2n+1)^2

For all n gt 1 , prove that 1^(2)+2^(2)+3^(2)+4^(2)+...........+n^(2) = (n(n+1)(2 n+1))/(6)

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

Using mathematical induction prove that 1^2+3^2+5^2+.....+(2n-1)^2=(n(2n-1)(2n+1))/3 for all n in N

For all nge1 , prove that p(n):n(n+1)(n+5) is divisible by 3.

For all nge1 , prove that p(n):2.7^n+3.5^n-5 is divisible by 24.