证明:对任意正整数n,不等式ln((n+2)/2)

问题描述:

证明:对任意正整数n,不等式ln((n+2)/2)

用数学归纳法证明:当n=1时,ln((1+2)/2)=ln(3/2)=1)不等式成立,即ln((k+2)/2)={[(k+2)/(k+1)]^(k+1)}^[1/(k+1)]=(k+2)/(k+1)=1+1/(k+1)>1+1/(k+2)
=(k+3)/(k+2)
所以当n=k+1(k>=1)时,(k+3)/2