已知函数f(x)=(1-2x)/(x+1)构造数列a(n)=f(n),n是正整数,求证a(n)>-2

问题描述:

已知函数f(x)=(1-2x)/(x+1)构造数列a(n)=f(n),n是正整数,求证a(n)>-2

f(x)=(1-2x)/(x+1)=(3-(2x+2))/(x+1)=3/(x+1)-2
n>0时,3/(n+1)>0
3/(n+1)-2>-2