![]() I’m open to new opportunities – consulting, contract or full-time – so let’s have a chat on how we can work together! Come follow me on Twitter: My other contact details can be found here. However, if you get really stuck, try searching for the phrase “forward differences”, and/or ‘finite differences” A mathematical sequence is a set of numbers written. I will leave it to the reader to prove why this method always work. In order to fully understand what a series means in math, it is helpful to first understand the idea behind a sequence. Suppose you have are given the first few terms of a sequence Derive and understand the formulae of General Term, Sum of the Series of n terms and remember standard results. ![]() It is actually easy to show by algebra that if a geometric sequence is constant. Start with basic theory, understand all the definition of the Sequences, series, and Arithmetic and geometric progression. This is a constant sequence that can be also considered an arithmetic sequence. I am hoping that the animated gif is fairly self-explanatory. Sequences and series is one of the easiest topics, you can prepare this topic without applying many efforts. Unlike some of my more lengthy posts, this is just a brief post about a nifty trick on how to easily fit a polynomial to a set of $N$ values. Lastly, well learn the binomial theorem, a powerful tool for expanding expressions. Well get to know summation notation, a handy way of writing out sums in a condensed form. If you are given the initial terms of a sequence, then here is an insanely simple method to derive a general formula for the first N terms, as well as the sum of the first N terms of the sequence. This unit explores geometric series, which involve multiplying by a common ratio, as well as arithmetic series, which add a common difference each time. In the explicit formula 'd(n-1)' means 'the common difference times (n-1), where n is the integer ID of term's location in the sequence.' Thankfully, you can convert an iterative formula to an explicit formula for arithmetic sequences. ![]()
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