Proving $\mathbb{P}(\xi_1+ \xi_2+...+\xi_n=1)=(\sum_{i=1}^{n}\lambda_i)\Delta + \mathcal{R}\Delta^2$
Show $P\{\xi_1+\dots+\xi_n=1\}=(\sum_{i=1}^n \lambda_i)\Delta + O(\Delta^2)$ (Shiryaev's Probability page 44)