Tìm các giới hạn sau: a) lim (1/1.3 + 1/3.5+....+ 1/(2k-1)(2k+1)

a) Do  12k−12k+1=12.2k+1−2k−12k−12k+1=1212k−1−12k+1

Suy ra  lim11.3+13.5+...+12k−12k+1

=lim1211−13+13−15+...+12n−1−12n+1=lim121−12n+1=12.