一道简便计算题:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.+100)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 12:51:39
![一道简便计算题:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.+100)](/uploads/image/z/1987627-67-7.jpg?t=%E4%B8%80%E9%81%93%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E9%A2%98%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.%2B1%2F%EF%BC%881%2B2%2B3%2B4%2B.%2B100%EF%BC%89)
一道简便计算题:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.+100)
一道简便计算题:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.+100)
一道简便计算题:1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.+100)
1/(1+2+3+…+100)=2/(100×101)=2/100-2/101
所以原式=1+2/2-2/3+2/3-2/4+.+2/100-2/101=2-2/101=200/101
不会