f(X)=(X+1)/(x-1),then[f(2)]+[f(3)]+[f(4)]+...+[f(99)]+[f(100)]=____

来源：百度知道编辑：UC知道时间：2024/06/30 01:48:19

[]是取整符号

f(x)=(x+1)/(x-1)=(x-1+2)/(x-1)=1+2/(x-1)
当0<2/(x-1)<1时
[f(x)]=1
这时x>4
那么
[f(2)]+[f(3)]+[f(4)]+...+[f(99)]+[f(100)]
=3++2+1*97
=102

[f(2)]+[f(3)]+[f(4)]+...+[f(99)]+[f(100)]
=|3/1|+|4/2|+|5/3|+```+|101/99|
=3+2+1*97
=102

从|5/3|之后取整都是1

x>=4,f(x)=1
[f(2)]+[f(3)]+[f(4)]+...+[f(99)]+[f(100)]=102