Show that `1/1.3+1/3.5+1/5.7+..........+n "terms"=n/(2n+1)`

Using the P.M.I 2prove that 1/1.3+1/3.5+1/5.7+....+n terms=n/(2n+1)

Show that 1^3/1+(1^3+2^3)/(1+3)+............n "terms "=n/24(2n^2+9n+13)

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

1.3+3.5+5.7+.....n terms =

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 by mathematical induction that 1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1)) = n/(2n+1),(n in N)

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

Prove by the method of Induction for all n in N : 1/3.5 + 1/5.7 + 1/7.9 + …. n terms = n/(3(2n+3))

(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....(n-1)terms

Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5))/48+n/(16(2n+1)) .