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The Taylor series is a method of turning non ‘nice’ polynomial functions into polynomial functions. By nice I mean: trigonometric, exponential, logarithmic. Now, this all probably sounds too good to be true and you may scratch your head in disbelief and ask yourself “How could it be possible to do…


Abstract

Following from the previous article I had written on the Taylor series here, in this article, I present a method for deriving the Leibniz product rule from Taylor’s theorem and Cauchy product rule.

Introduction

The Leibniz rule gives us a nice closed form for the nth derivative of the product of…


In problem-solving,

There is a preconceived notion that mathematics is a subject for the gifted or very intelligent, that the whole idea is having hundreds of equations on a blackboard with symbols flying here and there. I’ll tell you here, that’s it not. …


Last time we calculated sums finite and infinite, applied calculus and counted using the geometric series. This time we will learn how we can apply derivatives onto the finite geometric series for evaluating other discrete sums. …

buraian

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