Do the same as algorithm $1,$ but now calculate the sum of the $2$ element array right after you calculate the $1$ element array, and same thing with the $3$ element array. Once you compute the sum of the subarray from A$[$i$]$ to A$[$j$],$ the sum of the subarray from A$[$i$]$ to A$[$j$+1]$ is just the previous sum you computed plus A$[$j$+1].$ Don$$t add up all of the previous values all over again.