lim(n->无穷)p(1+r/n)^(nt)=lim(n->无穷)p[(1+r/n)^(n/r)]^(rt)=(pe)^(rt)最后一步怎么得出来的,(1+1/x)^x=e,(1+r/n)^(n/r)怎么会等于e呢?

Question

lim(n->无穷)p(1+r/n)^(nt) =lim(n->无穷)p[(1+r/n)^(n/r)]^(rt) =(pe)^(rt)
最后一步怎么得出来的,(1+1/x)^x=e,(1+r/n)^(n/r)怎么会等于e呢?

Answer 1

e= lim (1+1/x)^x x趋向正无穷大
这里n趋向无穷大时,n/r也是趋向无穷大的,做变量代换 x = n/r
连续函数满足极限复合运算规律.