1. ## Recursive Project

$\displaystyle \sum_{j=m}^n x_j$.
Well, we see that if $\displaystyle S_n = \sum_{j=1}^n x_j$, then $\displaystyle \sum_{j=m}^n x_j = S_m - S_n$ and each $\displaystyle S_n = S_{n-1} + x_n$.