if an initial amount A_{0}of money is invested at an interest ratercompoundedntimes a year, the value of the investment aftertyears is

A = A_{0}(1 + r/n )^{nt}

if we let n->infinity we refer to the continuous compounding of interest, use L' Hospital's Rule to show that if interest is compounded continuously, then the amount aftertyears is

A = A_{0}e^{rt .....i dont understand how to get from the first amount to the second using l' hospital's rule}