第1个回答 2009-08-22
通项=(n(n+1)-1)/n(n+1)=1-1/n(n+1)=1-(1/n-1/(n+1))
1<=n<=99
1/2+5/6+11/12+19/20+...+9701/9702+9899/9900
=1-(1-1/2)+1-(1/2-1/3)+1-(1/3-1/4)+1-(1/4-1/5)+...+1-(1/98-1/99)+1-(1/99-1/100)
=99-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100)
=99-(1-1/100)
=9801/100本回答被提问者采纳