奥数简便运算:(1/1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+.+(9/1
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/17 12:10:26
奥数简便运算:(1/1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+.+(9/1-8/2+7/3-6/4+.+1/9
![奥数简便运算:(1/1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+.+(9/1](/uploads/image/z/7761163-67-3.jpg?t=%E5%A5%A5%E6%95%B0%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%EF%BC%9A%281%2F1%2B%EF%BC%882%2F1-1%2F2%EF%BC%89%2B%EF%BC%883%2F1-2%2F2%2B1%2F3%EF%BC%89%2B%EF%BC%884%2F1-3%2F2%2B2%2F3-1%2F4%EF%BC%89%2B.%2B%289%2F1)
原式
=(1+2+3+4+5+6+7+8+9)-(1+2+3+4+5+6+7+8)/2+(1+2+3+4+5+6+7)/3-(1+2+3+4+5+6)/4+(1+2+3+4+5)/5-(1+2+3+4)/6+(1+2+3)/7
-(1+2)/8+1/9
=45-36/2+28/3-21/4+15/5-10/6+6/7-3/8+1/9
=45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
=30-45/8+6/7+70/9
=30+1517/504
=33+5/504
=(1+2+3+4+5+6+7+8+9)-(1+2+3+4+5+6+7+8)/2+(1+2+3+4+5+6+7)/3-(1+2+3+4+5+6)/4+(1+2+3+4+5)/5-(1+2+3+4)/6+(1+2+3)/7
-(1+2)/8+1/9
=45-36/2+28/3-21/4+15/5-10/6+6/7-3/8+1/9
=45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
=30-45/8+6/7+70/9
=30+1517/504
=33+5/504
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