# Maclaurin series

Prerequisite – Taylor theorem and Taylor series

We know that formula for expansion of Taylor series is written as:

Now if we put a=0 in this formula we will get the formula for expansion of Maclaurin series. T
hus Maclaurin series expansion can be given by the formula –

Maclaurin series expansion of some elementary functions :

1. Exponential function :

Differentiating n times,
So we get
Thus
2. f(x) = cos x
…..
3. f(x) = sin x
4. f(x) = (ax + b)^m
5. f(x) = ln(1+x)
6. f(x) = ln(1-x)

Example-1:
Find the first seven terms of f(x) = ln(sec x).

Explanation :

Differentiating w.r.t. x,

Thus we get the Maclaurin series as –

Example-2:
Evaluate Maclaurin series for tan x.

Explanation :

Thus we get Maclaurin series as –

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