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：2024/05/14 04:35:26
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?

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