To give u a hint,  the first 100th sum consists of only two terms N2 and N99 since all the other terms cancel out. There is a very easy method to calculate it. The only terms involved in the final calculation depend upon N1 and N2 only. It's not even necessary to calculate N99.  

If it's not a physics problem but a numerical analysis problem then you can solve it by writing a simple script using either iteration or recursion. It would be similar to solving a Fibonacci Series.

-Cowboy