![]() ![]() The difference of the sequence is constant and equals the difference between two consecutive terms. So we have just proven that this recursive function does indeed produce 3^n - 1. Find the common difference by subtracting any term in the sequence from the term that comes after it. ![]() Mathematica (or even the free WolframAlpha) has a recurrence solver, which with RSolve[ - 1) + 4.above, which I wrote out by hand and probably made some mistake, because (see 8) so as per this page, rational functions are nice because you can transform them into polynomials and use linear methods of step 1.It comes from the same root as the word recur, and is a technique that involves repeatedly applying a self-referencing definition until we reach some initial terms that are explicitly defined, and then going back through the. as I dove deeper for nonlinear stuff, I saw this page, using which I failed at z-transforms approach and didn't try linear algebra, but the link to rational difference eqn was the best (see next step) You may be familiar with the term recursion as a programming technique.(while I'm on the book topic) templatetypedef mentioned Concrete Mathematics, download here, but I don't know much about it except it has a recurrence, sums, and GF chapter (among others) and a table of simple GFs on page 335.if the previous example didn't make sense, download GF book and read the simplest GF example (section 1.1, ie a= 2 a+1, then 1.2, a= 2 a+1, then 1.3 - Fibonacci).The closed-form solution is a function of n which is obtained from the recursive relation which is a function of the previous terms f (n-1). ![]() if you want to read something about GF, go to this wiki, but I didn't get it till I started doing examples (see next) The Recursive Sequence Calculator is an online tool that calculates the closed-form solution or the Recurrence equation solution by taking a recursive relation and the first term f (1) as input.if your recurrence is linear (or polynomial), wikihow has step-by-step instructions (with and without GF).Let’s consider the sequence of numbers 3, 8, 13, 18, 23, and so on. In this video, we are going to discuss what each of them are and how to write sequences of numbers using each of these two techniques. not linear (nor polynomial), but also not completely nonlinear - it is a rational difference equation) Transcript Recursive formulas and explicit formulas are two ways of expressing arithmetic and geometric sequences of numbers. So after a full day of searching, I found the answer and hopefully these findings will be of help to others. Ok, I know you didn't want generating functions (GF from now on) and all the complicated stuff, but my problem turned out to be nonlinear and simple linear methods didn't seem to work. ![]()
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