1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 03:19:10
1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=

1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=
1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=

1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=
1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399
=1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/17+1/17-1/19+1/19-1/21)
=1/2×(1-1/21)
=1/2×20/21
=10/21

1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399
=1/2(1-1/3+1/3-1/5+...+1/19-1/21)
=1/2*20/21
=10/21

0.476190476190

原式=1/(1*3)+1/(3*5)+1/(5*7)+……+1/(19*21)
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/19-1/21)]/2
=(1-1/3+1/3-1/5+……+1/19-1/21)/2
=(1-1/21)/2
=(20/21)/2
=10/21
=0.476190476190……