简便运算1/2+5/6+11/12+19/20...+80/90+109/110

简便运算1/2+5/6+11/12+19/20...+80/90+109/110
简便运算1/2+5/6+11/12+19/20...+80/90+109/110

简便运算1/2+5/6+11/12+19/20...+80/90+109/110
1/2+5/6+11/12+19/20...+80/90+109/110
=（1-1/2 ）+（1-1/6）+.+(1- 1/90)+(1- 1/110)
= 10 - (1/2 + 1/6+ .+ 1/90 + 1/110)
=10 -(1- 1/2 +1/2 - 1/3 + .+ 1/9- 1/10 + 1/10 -1/11)
=10- (1- 1/11)
=10- 10/11
=100/11
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1/2+5/6+11/12+19/20...+80/90+109/110
=1-1/2+1-1/6+1-1/12+1-1/20+....+1-1/110
=1×10-(1/1×2＋1/2×3＋1/3×4＋....+1/10×11)
=10-(1-1/2+1/2-1/3+...+1/10-1/11)
=10-(1-1/11)
=10-1+1/11
=9+1/11
=100/11

1/2+5/6+11/12+19/20...+80/90+109/110
=1-1/2+1-1/6+1-1/12+1-1/20+....+1-1/110
=1×10-(1/1×2＋1/2×3＋1/3×4＋....+1/10×11)
=10-(1-1/2+1/2-1/3+...+1/10-1/11)
=10-(1-1/11)
=10-1+1/11
=9+1/11
=100/11
望采纳！！