帮忙做一道简便运算1/1+(2/1-1/2)+(3/1-2/2+1/3)+(1/4-3/2+2/3-1/4)+...+(
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/06/28 06:39:56
帮忙做一道简便运算
1/1+(2/1-1/2)+(3/1-2/2+1/3)+(1/4-3/2+2/3-1/4)+...+(9/1-8/2+7/3-6/4+...+1/9)
1/1+(2/1-1/2)+(3/1-2/2+1/3)+(1/4-3/2+2/3-1/4)+...+(9/1-8/2+7/3-6/4+...+1/9)
![帮忙做一道简便运算1/1+(2/1-1/2)+(3/1-2/2+1/3)+(1/4-3/2+2/3-1/4)+...+(](/uploads/image/z/16688976-24-6.jpg?t=%E5%B8%AE%E5%BF%99%E5%81%9A%E4%B8%80%E9%81%93%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%971%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%881%2F4-3%2F2%2B2%2F3-1%2F4%EF%BC%89%2B...%2B%EF%BC%88)
1/1+(2/1-1/2)+(3/1-2/2+1/3)+(1/4-3/2+2/3-1/4)+...+(9/1-8/2+7/3-6/4+...+1/9)
=[1/1+2/1+3/1+...+9/1]-[1/2+2/2+3/2+...+8/2]+[1/3+2/3+...+7/3]-[1/4+2/4+...+6/4]+[1/5+2/5...+5/5]-[1/6+2/6+3/6+4/6]+[1/7+2/7+3/7]-[1/8+2/8]+1/9
=[1+9]*9/2-[1+8]*8/2/2+[1+7]*7/2/3-[1+6]*6/2/4+[1+5]*5/2/5-10/6+6/7-3/8+1/9
=45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
=16637/504
=33又5/504
=[1/1+2/1+3/1+...+9/1]-[1/2+2/2+3/2+...+8/2]+[1/3+2/3+...+7/3]-[1/4+2/4+...+6/4]+[1/5+2/5...+5/5]-[1/6+2/6+3/6+4/6]+[1/7+2/7+3/7]-[1/8+2/8]+1/9
=[1+9]*9/2-[1+8]*8/2/2+[1+7]*7/2/3-[1+6]*6/2/4+[1+5]*5/2/5-10/6+6/7-3/8+1/9
=45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
=16637/504
=33又5/504
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