1/2+5/6+11/12+19/20+.+9899/9900详解

问题描述:

1/2+5/6+11/12+19/20+.+9899/9900详解

1/2+5/6+11/12+19/20+....+9899/9900
=1-(1/2)+1-(1/6)+……+1-1/9900
=(1+1+……+1)-[(1/2)+(1/6)+……+(1/9900)]
=99-[1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+……(1/99)-(1/100)]
=99-(99/100)
=

原式=1-1/2+1-1/6+1-1/12+1-1/20+…………+1-1/9900
=99-﹙1/2+1/6+1/12+1/20+……+1/9900﹚
=99-﹙1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100﹚
=99-﹙1-1/100﹚
=99-1+1/100
=98+1/100
=98又1/100.