比较难的求极限题目(只要思路) 为什么lim(n趋向于无穷)1/n*{(n+1)(n+2).(n+n)}^(1/n)=4/e?

问题描述:

比较难的求极限题目(只要思路) 为什么lim(n趋向于无穷)1/n*{(n+1)(n+2).(n+n)}^(1/n)=4/e?

为了就算方便,令A=(1/n)[(n+1)(n+2)(n+3).(n+n)]^(1/n)则 A=[(n+1)(n+2)(n+3).(n+n)/n^n]^(1/n)={[(n+1)/n][(n+2)/n][(n+3)/n].[(n+n)/n]}^(1/n)=[(1+1/n)(1+2/n)(1+3/n).(1+n/n)]^(1/n)∴lnA=(1/n)[ln(1+1/n)+ln(1+...