Let f(N)=N\left(\frac{9}{10}\right)^{N}, and let \frac{m}{n} denote the maximum value of f(N), as N ranges over the positive integers. If m and n are relatively prime positive integers, find the remainder when m+n is divided by 1000.
Let f(N)=N\left(\frac{9}{10}\right)^{N}, and let \frac{m}{n} denote the maximum value of f(N), as N ranges over the positive integers. If m and n are relatively prime positive integers, find the remainder when m+n is divided by 1000.