求证lim(1+1/n+1/n2)n =e ( n→∞)

问题描述:

求证lim(1+1/n+1/n2)n =e ( n→∞)
式中的2是平方!

lim(1+1/n+1/n2)n=lim e(n ln(1+1/n+1/n2) )
lim(n+1/n)n =e
lim e (n ln(n+1/n) )=e
所以求证