Question

s=1/1*3+1/3*5+1/5*7+...+1/((2*n-1)*(2*n+1))

Answer 1

S = 1/1 - 1/3 + 1/3 - 1/5 + ...-1/(2n - 1) + 1/(2n - 1)  - 1/(2n + 1)
S = 1 - 1/(2n + 1);
S = (2n + 1 - 1)/2n+1
S = 2n/2n + 1;