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

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/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....+n))=(2n)/((n+1))

Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......+1/((2n+1)(2n+3))=n/(3(2n+3) for all n in N

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

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

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

Using mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......+1/((3n-1)(3n+2))=n/(6n+4) for all n in N .

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

Using mathematical induction prove that 1cdot3+3cdot5+5cdot7+.....+(2n-1)(2n+1)=(n(4n^2+6n-1))/3 true for all n in N