Calculate the Maclaurin series expansion for common functions.
Calculate
Series Expansion
Expansion
1 + x^1/1 + x^2/2 + x^3/6 + x^4/24
Approximation at x2.70833For x = 1
About this calculator
What is a Maclaurin Series?
A Maclaurin series is a Taylor series expansion of a function about 0. It represents a function as an infinite sum of terms calculated from the values of its derivatives at a single point (x=0).
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Pro Tips
Convergence: The series only converges to the function value within a specific radius of convergence.
Accuracy: More terms generally provide a better approximation near x=0.
Applications: Used in physics and engineering to approximate complex functions.
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Fun Facts
"Named after Colin Maclaurin, a Scottish mathematician."
"It is a special case of the Taylor Series where a = 0."
"Euler used these series to solve the Basel problem."
