大师作文网简便计算：1/35+1/63+1/99+1/143
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/09/20 07:50:16
简便计算：1/35+1/63+1/99+1/143
1/35+1/63+1/99+1/143
=1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=(1/2)*[(1/5)-(1/7)]+(1/2)*[(1/7)-(1/9)]+(1/2)*[(1/9)-(1/11)]+(1/2)*[(1/11)-(1/13)]
=(1/2)*[(1/5)-(1/7)+(1/7)-(1/9)+(1/9)-(1/11)+(1/11)-(1/13)]
=(1/2)*[(1/5)-(1/13)]
=(1/2)*(8/65)
=4/65.
=1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=(1/2)*[(1/5)-(1/7)]+(1/2)*[(1/7)-(1/9)]+(1/2)*[(1/9)-(1/11)]+(1/2)*[(1/11)-(1/13)]
=(1/2)*[(1/5)-(1/7)+(1/7)-(1/9)+(1/9)-(1/11)+(1/11)-(1/13)]
=(1/2)*[(1/5)-(1/13)]
=(1/2)*(8/65)
=4/65.