Đặt A=1/1.2.3+1/2.3.4+...+1/99.100.101
2A=2/1.2.3+2/2.3.4+...2/99.100.101
2A=3-1/1.2.3+4-2/2.3.4+...+101-99/99.100.101
2A=3/1.2.3-1/1.2.3+4/2.3.4-2/2.3.4+...+101/99.100.101-99/99.100.101
2A=1/1.2-1/2.3+1/2.3-1/3.4+...+1/99.100-1/100.101
2A=1/2-1/10100