1/51*1/53+1/53*1/55+……1/99*1/101等于?【1/51是51分之1,*是乘号】1/51*1/53+1/53*1/55+……1/99*1/101
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![1/51*1/53+1/53*1/55+……1/99*1/101等于?【1/51是51分之1,*是乘号】1/51*1/53+1/53*1/55+……1/99*1/101](/uploads/image/z/241004-20-4.jpg?t=1%2F51%2A1%2F53%2B1%2F53%2A1%2F55%2B%E2%80%A6%E2%80%A61%2F99%2A1%2F101%E7%AD%89%E4%BA%8E%3F%E3%80%901%2F51%E6%98%AF51%E5%88%86%E4%B9%8B1%2C%2A%E6%98%AF%E4%B9%98%E5%8F%B7%E3%80%911%2F51%2A1%2F53%2B1%2F53%2A1%2F55%2B%E2%80%A6%E2%80%A61%2F99%2A1%2F101)
1/51*1/53+1/53*1/55+……1/99*1/101等于?【1/51是51分之1,*是乘号】1/51*1/53+1/53*1/55+……1/99*1/101
1/51*1/53+1/53*1/55+……1/99*1/101等于?【1/51是51分之1,*是乘号】
1/51*1/53+1/53*1/55+……1/99*1/101
1/51*1/53+1/53*1/55+……1/99*1/101等于?【1/51是51分之1,*是乘号】1/51*1/53+1/53*1/55+……1/99*1/101
规律:
1/n × 1/(n+d) = 1/d × [1/n - 1/(n+d)]
可以自己把右侧的式子进行通分验证结论的正确性.
1/51*1/53+1/53*1/55+……1/99*1/101
=1/2 × [1/51 - 1/53 +1/53-1/55 +……+1/99-1/101]
=1/2 × (1/51 - 1/101)
=1/2 × 50/5151
=25/5151
原式=1/2(1/51-1/53+1/53-1/55+……+1/97-1/99+1/99-1/101)
=1/2*(1/51-1/101)=25/5151
=1/2(1/51-1/53+1/53-1/55+……1/99-1/101)
=1/2(1/51-1/101)
=25/5151
1/161368136187641824614646874618461928121131456
原式=0.5*(1/51-1/53)+0.5*(1/53-1/55)+...0.5*(1/99-1/101)
=0.5(1/51-1/53+1/53-1/55+....1/99-1/101)
=0.5*(1/51-1/101)
=25/5151