Naively summing an alternating series

Suppose you run across the power series for the exponential function and decide to code it up. Good idea: you’ll probably learn something, though maybe not what you expect. Maybe you decide a tolerance of 10−12 is good enough, and so you sum the terms until the next term to add is below the tolerance. from math import factorial, exp def naive_exp(x): tolerance = 1e-12 s = 0 n = 0 while True: delta = x**n / factorial(n) s += delta if abs(delta) < tolerance: return s n += 1 You want to try your program out, so you compute e by calling the function at 1. If you compare this to calling exp(1) you find that you got all the digits correct. Now you try computing exp(-20). Calling naive_exp(-20) gives 5.47893091802112e-10 but calling exp(-20) gives 2.061153622438558e-09 Don’t brush things like this as flukes or compiler bugs [1]. This is your golden opportunity to learn something. Maybe you add a print statement to see the intermediate values of the sum stored in the variable s. If you do,…