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)

(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms

Using the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .

underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(2n+1))}=

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

1+ 3+ 7 + 15… n terms =

lim_(n to infty) ((1)/(3.7)+(1)/(7.11) +(1)/(11.15)+. . . +(n" terms ")) =