I want to calculate the sum:
$$\sum_{k=1}^{1000} \frac{\lambda_1^k\exp(-\lambda_1)}{k!}(1-\sum_{n=0}^{k-1} \frac{1}{n!}exp(-\lambda_2 x)(\lambda_2 x)^n)$$
Wolfram Alpha seems to be having trouble with the second summation, I think the problem is that the stopping point of the second summation depends on the first summation. Is Wolfram Alpha able to solve this summation or is there different software I can use?