初一新生数学题目.简便计算:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+···+1/(1+2+3+4
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/07 01:34:42
初一新生数学题目.
简便计算:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+···+1/(1+2+3+4+···+100)
简便计算:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+···+1/(1+2+3+4+···+100)
![初一新生数学题目.简便计算:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+···+1/(1+2+3+4](/uploads/image/z/18203439-39-9.jpg?t=%E5%88%9D%E4%B8%80%E6%96%B0%E7%94%9F%E6%95%B0%E5%AD%A6%E9%A2%98%E7%9B%AE.%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%EF%BC%9A1%2B1%2F%EF%BC%881%2B2%EF%BC%89%2B1%2F%EF%BC%881%2B2%2B3%EF%BC%89%2B1%2F%EF%BC%881%2B2%2B3%2B4%EF%BC%89%2B%C2%B7%C2%B7%C2%B7%2B1%2F%EF%BC%881%2B2%2B3%2B4)
等式= 2/(1*2) + 2/(2*3) + 2/(3*4) + .+2/(100*101)
= 2*(1/(1*2)+1/(2*3) + 1/(3*4)+.1/(100*101))
=2*(1-1/2+1/2-1/3+1/3-1/4+.+1/100-1/101)
= 2*(1-1/101)
=200/101
= 2*(1/(1*2)+1/(2*3) + 1/(3*4)+.1/(100*101))
=2*(1-1/2+1/2-1/3+1/3-1/4+.+1/100-1/101)
= 2*(1-1/101)
=200/101
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