Lecture
Geometric Series: Basic Example
Description
This lecture introduces the basic example of a geometric series, where the function is defined as f(x)=1/(1-x) for x in the interval ]-1,1[. The Taylor formula is derived, showing f(x) = Σ(2^n)x^n for n=0 to infinity. The convergence radius is discussed, highlighting the convergence for x in ]-1,1[. The lecture also explores the divergence of the series for x=1. Various examples and calculations are provided to illustrate the concepts.
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