= 5/2 . ( 5-5/3+5/3-5/5+5/5-5/7+. . .+5/99-5/100
=5/2 . (5-5/100)
=5/2 . 99/20
= 99/8
mk nghĩ đổi 5/3.7 thành 5/5.7 thì sẽ dễ giải hơn như thế này này:
5/1.3+5/3.5+5/5.7+....+5/99.101
=5.2/1.3.2+5.2/3.5.2+5.2/5.7.2+.....+5.2/99.101.2
=5/2(2/1.3+2/3.5+2/5.7+...+2/99.100)
=5/2(2/1-2/3+2/3-2/5+2/5-2/7+....+2/99-2/101)
=5/2(2/1-2/101)
=5/2(202/101-2/101)
=5/2.200/101=1000/202=500/101