📚 Maclaurin Series for 1/(1 + x) – Step-by-Step Example 📚
In this video, I walk through the process of finding the Maclaurin series for the function f(x) = 1/(1 + x), centered at a = 0. This classic example shows how to calculate the series by determining the necessary derivatives and then using the Maclaurin series formula to expand the function as a power series.
🚀 What’s covered:
Understanding the Maclaurin series as a specific type of Taylor series when a = 0.
Step-by-step calculation of the derivatives of 1/(1 + x) at x = 0.
Constructing the series expansion and identifying the resulting pattern.
This is a fundamental example that ties into many other areas of calculus and series expansions, making it important for understanding power series and approximations.
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