Notice that thus far, of course, I’ve made no use the fact that I’m constantly recalculating the intemediate values from 1 to n. If those values were cached, of course, I could save myself a lot of computations. One way to do this is to use recursion, but if we’ve already ca...
Let the sequence \{ a_n \}_{n \in N} defined by the recursion a_{n-1} = \sqrt{2 + a_n} with a_1 = 1 . Show by induction that \{ a_n \}_{n \in N} is an increasing sequence. Show by induc Let a_1 =...
It could be made faster - for example it uses recursion to calculate the factorial of 16. I could do that without recursion. Sometimes the problem you run into with these raw CPU benchmarks is that the compiler tries to "help" you by optimizing away all of your code if it doesn't re...