搜搜做题作业网计算1/3+1/15+1/35+1/63+1/99+1/143+1/195+255+1/323+1/399
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/05/08 18:49:13
计算1/3+1/15+1/35+1/63+1/99+1/143+1/195+255+1/323+1/399
2*（1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323+1/399）
=2/3+2/15+2/35+2/63+2/99+2/143+2/195+2/255+2/323+2/399
=(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)
=1-1/21
=20/21
∴ 1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323+1/399=10/21
=2/3+2/15+2/35+2/63+2/99+2/143+2/195+2/255+2/323+2/399
=(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)
=1-1/21
=20/21
∴ 1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323+1/399=10/21