Maclaurin series

 You have learnt about Maclaurin series in your school but sometimes it's difficult to understand the topic so my purpose of writing on Maclaurin series is to make it easy for you. After reading this article you will have clear picture of this topic in your mind.

Maclaurin series 

Definition

Maclaurin series is defined as the expansion of power series.

A function f(X) such that 

f(0) is defined and all the derivatives of f(X) is defined at X=0 is the maclaurin series of that function.

OR

A function that has expansion series that gives the sum of derivatives of that function.

Formula:-

That's what you have learnt in school but now I am gonna explain this in simple words.

In simple words

It provides the general formula of any function independent of a fixed point by finding the coefficients of the function using differentiation.

For example:-

Maclaurin series of e^x 

 If we see th graph of e^x and after expanding this function by Maclaurin series we get a series equation of this function, this would have approximately same graph as e^x.

Graph:-

Graph of e^x and it's Maclaurin series

You can see here as we are taking more expanded terms the graph is getting approximately same of the series as the original function e^x.

Why use Maclaurin series?

You are probably thinking why we use Maclaurin series of a function instead of that function.

So the answer is Maclaurin series are usually used in computation like if you wanna make a calculator and you want to put (log function) in your calculator so you need programming to make calculator so there (in programming) you will use Maclaurin series of (log function) instead of the original function as it is.

I hope now you will have clear picture of Maclaurin series in your mind.

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