Introduction to Probability · Problem 12.1.1

Random Walks — Grinstead & Snell

Mathematics — Probability · random-walks-generating-functions

Problem

Using the Binomial Theorem, show that 11−4x=∑m=0∞(2mm)xm.\frac{1}{\sqrt{1-4x}} = \sum_{m=0}^{\infty} \binom{2m}{m} x^m. What is the interval of convergence of this power series?

Related theory

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