1.1 1 1 1
------ + -----＋------+...+ -------
1×2 2×3 3×4 99×100
=1-1/2 +1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100
2.1 1 1 1 1 1 1 1
-- + --- + --- + --- + --- + —— ＋—— +——
3 6 10 15 21 28 36 45
=(1/3+1/6+1/36)+(1/10+1/15+1/45)+(1/21+1/28)
=19/36+17/90+1/12
=(190+68+30)/360
=288/360
=4/5
3.1+3+5+.+17+19
——————————
2+4+6.+18+20
=(1+3+5+……+17+19）/(2+4+6+……+18+20）
=[（1+19）*10/2]/[(2+20)*10/2]
=20/22
=10/11
4.135×271+136
------------
136×271-135
=(135*271+136)/(136*271-135)
=[271(136-1)+136]/(136*271-135)
=[271*136-135]/(136*271-135)
=1
5.1 3 2 5 7 9 10 11 19
--- + ---- + ---- + ---- + ---- + ---- + ---- + --- + ---
3 4 5 7 8 20 21 24 35
=(1/3+5/7+10/21)+(3/4+7/8+11/24)+(2/5+9/20+19/35)
=32/21+50/24+195/140
=1+11/21+2+1/12+1+11/28
=4+(11/21+1/12+11/28)
=4+(132+21+99)/252
=4+1
=5 .
6.1 1 1 1 1 1
--- + --- + ---- +--- + ---- + ---
2 6 12 20 30 42
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7