Exercise 2.8.1

By inspection $s_{\mathit{nn}}=-2+1∕2^{n-1}$, so $\underset{n\to \infty }{\lim <!--\; FUNCTION\; APPLICATION\; -->}{s}_{\mathit{nn}}=-2$. This is the same as the result when fixing $j$ and summing down each column, since each column series has finitely many non-zero elements.