1/2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+.+1/39.40

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 10:43:55
1/2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+.+1/39.40

1/2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+.+1/39.40
1/2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+.+1/39.40

1/2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+.+1/39.40
1/2+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+.+1/(39*40)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/39-1/40
=1-1/40=39/40