求三分之一+十五分之一+三十五分之一+七十七分之一+一百四十三分子一
三分之一+十五分之一+三十五分之一+七十七分之一+一百四十三分子一
=1/(1x3) +1/(3x5) +1/(5x7) +1/(7x11)+1/(11x13)
=(1-1/3+1/3-1/5+1/5-1/7)/2+(1/7-1/11)/4+(1/11-1/13)/2
=(1-1/7)*2/4+(1/7-1/11)/4+(1/11-1/13)*2/4
=(2-2/7+1/7-1/11+2/11-2/13)/4
=(2-1/7+1/11-2/13)/4
=(2-11/77+7/77-2/13)/4
=(1-2/77-1/13)/2
=(1001-2*13-77)/2002
=898/2002
=449/1001
望采纳哦
答案就是449/1001.l
1/3+1/15+1/35+1/77+1/143=1/3*1+1/3*5+1/5*7+1/7*11+1/11*13=.....=449/1001
裂项相减法
1/3+1/15+1/35+1/77+1/143
=1/3+(1/3-1/5)*1/2+(1/5-1/7)*1/2+(1/7-1/11)*1/4+(1/11-1/13)*1/2
=1/3+1/3*1/2-1/5*1/2+1/5*1/2-1/7*1/2+1/7*1/4-1/11*1/4+1/11/1/2-1/13*1/2
=(1+1/2)*1/3-(1/2-1/2)*1/5-(1/2-1/4)*1/7+(1/2-1/4)/1/11-1/26
=1/2-0-(1/7-1/11)*1/4-1/26
=1/2-(1/77+1/26)
=1/2-103/2002
=898/2002
=449/1001
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