Problem $1(15$ points$)$

Consider a function called computeSum that takes as input a positive integer $n$ and returns the ${\displaystyle \underset{?}{\overset{?}{}}}S(n)={\displaystyle \underset{k=1}{\overset{2n}{}}}k(k-5).$ Design a recursive algorithm with the smallest possible number of base cases and recursive cases. For full credit, each case should also minimize the number of atomic operations. Use the algorithm in the next problem as a starting point for typesetting yours in $L^A{T}_{E}x.$

Write down your pseudocode in this box.

Then justify $($also in this box$)$ the arithmetic used in your pseudocode.