(1)1-1/2-1/6-1/12-1/20-...-1/9900(2)1/2+1/6+1/12+1/20+...+1/9900(3)1/3+1/15+1/35+1/63+...+1/9999

问题描述:

(1)1-1/2-1/6-1/12-1/20-...-1/9900(2)1/2+1/6+1/12+1/20+...+1/9900(3)1/3+1/15+1/35+1/63+...+1/9999

(1)1-1/2-1/6-1/12-1/20-...-1/9900
=1/2-(1/2-1/3)-(1/3-1/4)-……-(1/99-1/100)
=1/2-1/2+1/3-1/3+1/4-……-1/99+1/100
=1/100
(2)1/2+1/6+1/12+1/20+...+1/9900
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100
(3)1/3+1/15+1/35+1/63+...+1/9999
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+……+1/99-1/101)
=1/2*(1-1/101)
=50/101