Question

$\frac{2}{1X3}$+$\frac{2}{3X5}$+...+$\frac{2}{(2n-1)(2n+1)}$,n∈N*

Answer 1

se transforma in 
(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...........+(1/(2n-1) -1/(2n+1)=
1/1-1/3+1/3-1/5+................+1/(2n-1) -1/(2n-1)=
1/1-1/(2n-1)=
(2n-1-1)/(2n-1)=2(n-1)/(2n-1)
(2n-1)/(2n-1) -1/(2n-1)=1-1/(2n-1)