figure series of recursive calls adding list of numbers itselfthis is the reason that we call the list_sum algorithm recursive recursive function is function that calls itself figure shows the series of recursive calls that are needed to sum the list [ you should think of this series of calls as series of simplifications each time we make recursive call we are solving smaller problemuntil we reach the point where the problem cannot get any smaller when we reach the point where the problem is as simple as it can getwe begin to piece together the solutions of each of the small problems until the initial problem is solved figure shows the additions that are performed as list_sum works its way backward through the series of calls when list_sum returns from the topmost problemwe have the solution to the whole problem the three laws of recursion like the robots of asimovall recursive algorithms must obey three important laws recursive algorithm must have base case recursive algorithm must change its state and move toward the base case recursive algorithm must call itselfrecursively let' look at each one of these laws in more detail and see how it was used in the list_sum algorithm firsta base case is the condition that allows the algorithm to stop recursing base case is typically problem that is small enough to solve directly in the list_sum algorithm the base case is list of length to obey the second lawwe must arrange for change of state that moves the algorithm toward the base case change of state means that some data that the algorithm is using is modified what is recursion