第1个回答 2012-03-06
1 原式=1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11+1/10-1/12+1/11-1/13=1/2+1/3-1/12-1/13=35/52
2 原式=1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90
=1+3+5+7+9+11+13+15+17+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=81+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8 +1/8-1/9
=81+1/2-1/9
=81又7/18
3 原式=2002*(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11)
=2002*(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)÷2
=2002*8/33÷2
8008/33本回答被提问者和网友采纳
第2个回答 2012-03-06
1/8+1/15+1/24+...+1/143=1/(2*4)+1/(3*5)+1/(4*6)+...+1/(11*13)=(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+...+1/11-1/13)/2=(1/2-1/12-1/13)/2
2、=1+3+5+7+9+11+13+15+17+19+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=100+1/2-1/3+1/3-1/4+...+1/9-1/10=100+1/2-1/10
3、=2002*(1/3+1/3*5+1/5*7+1/7*9+1/9*11)=2002*(1/1-1/3+1/3-1/5+...+1/9-1/11)/2=1001*10/11
第3个回答 2012-03-06
(1)=1/2(1/2-1/4+1/3-1/5+1/4-1/6+......+1/11-1/13)=(1/2)*(1/2+1/3-1/12-1/13)=35/104
(2)=1+3+5+7+9+11+13+15+17+(1/2-1/3+1/3-1/4+1/4-1/5+......1/9-1/10)=81又五分之二
(3)=1001(10/11)=910
第4个回答 2012-03-06
1 将n^2-1=(n+1)(n-1) 那么1/(n^2-1)=1/2X[1/(n-1)-1/(n+1)]
前后项抵消得 1/2X[1/2+1/3-1/12-1/13]=35/104
(2)(2)=1+3+5+7+9+11+13+15+17+(1/2-1/3+1/3-1/4+1/4-1/5+......1/9-1/10)=81又五分之二
(3)=1001(10/11)=910