1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+.+1/(1*2*3*4*...*50)怎么做?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 05:22:25
![1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+.+1/(1*2*3*4*...*50)怎么做?](/uploads/image/z/11473970-50-0.jpg?t=1%2F%281%2A2%29%2B1%2F%281%2A2%2A3%29%2B1%2F%281%2A2%2A3%2A4%29%2B.%2B1%2F%281%2A2%2A3%2A4%2A...%2A50%29%E6%80%8E%E4%B9%88%E5%81%9A%3F)
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+.+1/(1*2*3*4*...*50)怎么做?
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+.+1/(1*2*3*4*...*50)怎么做?
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+.+1/(1*2*3*4*...*50)怎么做?
原式=1/(2*3/2)+1/(3*4/2)+……+1/(50*51*/2)
=1/2*(1/2-1/3+1/3-1/4+……+1/50-1/51)
=1/2*(1/2-1/51)
=49/204