四道简算
1.1989×1999-1988×20002.1/15+1/35+1/63+1/99+1/143+1/1953.4/3-7/12+9/20-11/30+13/42-15/...
1. 1989×1999-1988×2000
2. 1/15+1/35+1/63+1/99+1/143+1/195
3. 4/3-7/12+9/20-11/30+13/42-15/56
4. 2/2×4+2/4×6+2/6×8+…+2/98×100 展开
2. 1/15+1/35+1/63+1/99+1/143+1/195
3. 4/3-7/12+9/20-11/30+13/42-15/56
4. 2/2×4+2/4×6+2/6×8+…+2/98×100 展开
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1. 1989×1999-1988×2000
=(1988+1)×1999-1988×2000
=1988×1999+1999-1988×2000
=1999-1988×(2000-1999)
=1999-1988
=1
2. 1/15+1/35+1/63+1/99+1/143+1/195
=1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)+1/2(1/13-1/15)
=1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2(1/3-1/15)
=2/15
3. 4/3-7/12+9/20-11/30+13/42-15/56
=1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=1-1/8
=7/8
4. 2/2×4+2/4×6+2/6×8+…+2/98×100
=1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100
=1/2-1/100
=49/100
=(1988+1)×1999-1988×2000
=1988×1999+1999-1988×2000
=1999-1988×(2000-1999)
=1999-1988
=1
2. 1/15+1/35+1/63+1/99+1/143+1/195
=1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)+1/2(1/13-1/15)
=1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2(1/3-1/15)
=2/15
3. 4/3-7/12+9/20-11/30+13/42-15/56
=1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=1-1/8
=7/8
4. 2/2×4+2/4×6+2/6×8+…+2/98×100
=1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100
=1/2-1/100
=49/100
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