About Maclaurin Series Formula
A Maclaurin series is a function that has expansion series that gives the sum of derivatives of that function. The Maclaurin series of a function up to order n may be found using Series 
.
It is a special case of Taylor series when x = 0. The Maclaurin series is given by The Maclaurin series formula is
Where,f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0. Function Maclaurin Series
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The Maclaurin series is a way to write a function as an infinite sum of terms. It's especially useful when you want to approximate a function using polynomials.
It is a special case of the Taylor series, where we expand the function around zero (x = 0).
What is the formula?
What do these symbols mean?
- f(x): the function you want to expand
- f'(0), f''(0), ...: the derivatives of the function at x = 0
- n!: means "n factorial", which is 1 × 2 × 3 × ... × n
- xⁿ: x raised to the power of n
Example: Maclaurin Series for eˣ
Let's use the formula for the function f(x) = e^x:
Since the derivative of e^x is always e^x, and e⁰ = 1, we get:
Why is it useful?
- Helps approximate hard functions with simpler polynomials.
- Used in calculus, physics, engineering, and computer science.
- Good for calculating values when a calculator isn’t available.