作业帮A mathematics problemQuestion:若n,n+1皆为正数,试比较n的n+1的次方与n+1的n次方的大小.（似乎要分类讨论）
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A mathematics problemQuestion:若n,n+1皆为正数,试比较n的n+1的次方与n+1的n次方的大小.（似乎要分类讨论）
A mathematics problem
Question:
若n,n+1皆为正数,试比较n的n+1的次方与n+1的n次方的大小.（似乎要分类讨论）
A mathematics problemQuestion:若n,n+1皆为正数,试比较n的n+1的次方与n+1的n次方的大小.（似乎要分类讨论）
这里n是整数吗?如果没有限制为整数,将比较麻烦
因是比较A=n^(n+1)与B=(n+1)^n
只需比较
lnA/[n(n+1)]=(ln n)/n
与
lnB/[n(n+1)]=[ln(n+1)]/(n+1)
考虑函数f(x)=lnx/x
则求导（理解求导吗?）得
f'(x)=(1-lnx)/x
当0
当x>e时则f'(x)<0
也就是说,f(x)在(0,+无穷大)上是先增后减,最高点于x=e处
那么
部分讨论如下：
1、n
3、e-1
(n+1)lgn与nlg(n+1)怎么比较呢
( lg n )/ n
分类讨论即可
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