简便运算,这里还有几道,不好意思,麻烦了①2009×2010-1/2009+2008×2010②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35③5/9×79又6/17+50×1/9+11/9×5/17④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/16 17:45:19
![简便运算,这里还有几道,不好意思,麻烦了①2009×2010-1/2009+2008×2010②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35③5/9×79又6/17+50×1/9+11/9×5/17④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400](/uploads/image/z/2736213-69-3.jpg?t=%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%2C%E8%BF%99%E9%87%8C%E8%BF%98%E6%9C%89%E5%87%A0%E9%81%93%2C%E4%B8%8D%E5%A5%BD%E6%84%8F%E6%80%9D%2C%E9%BA%BB%E7%83%A6%E4%BA%86%E2%91%A02009%C3%972010-1%2F2009%2B2008%C3%972010%E2%91%A11%2F3%2B3%2F4%2B2%2F5%2B5%2F7%2B7%2F8%2B9%2F20%2B10%2F21%2B11%2F24%2B19%2F35%E2%91%A25%2F9%C3%9779%E5%8F%886%2F17%2B50%C3%971%2F9%2B11%2F9%C3%975%2F17%E2%91%A31%C3%972%C3%973%2B2%C3%974%C3%976%2B...%2B100%C3%97200%C3%97300%2F2%C3%973%C3%974%2B4%C3%976%C3%978%2B...%2B200%C3%97300%C3%97400)
简便运算,这里还有几道,不好意思,麻烦了①2009×2010-1/2009+2008×2010②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35③5/9×79又6/17+50×1/9+11/9×5/17④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
简便运算,这里还有几道,不好意思,麻烦了
①2009×2010-1/2009+2008×2010
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
③5/9×79又6/17+50×1/9+11/9×5/17
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
简便运算,这里还有几道,不好意思,麻烦了①2009×2010-1/2009+2008×2010②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35③5/9×79又6/17+50×1/9+11/9×5/17④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
①2009×2010-1/2009+2008×2010
=(2009×2010-1)/(2009+(2009-1)(2009+1))
=(2009×(2009+1)-1)/(2009+2009²-1)
=(2009²+2009-1)/(2009²+2009-1)
=1;
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
=1/3+3/4+2/5+5/7+7/8+(4+5)/20+(3+7)/21+(3+8)/24+(14+5)/35
=1/3+3/4+2/5+5/7+7/8+1/5+1/4+1/7+1/3+1/8+1/3+2/5+1/7
=(1/3+1/3+1/3)+(3/4+1/4)+(2/5+1/5+2/5)+(5/7+1/7+1/7)+(7/8+1/8)
=1+1+1+1+1
=5;
③5/9×79又6/11+50×1/9+11/9×5/17
=(5/9)×(79+6/11+50+5/11)
=(5/9)×130
=650/9;
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
=(1×2×3+2×4×6+...+100×200×300)/4×(1×2×3+2×4×6+...+100×200×300)
=1/4;
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