proof of binomial formula

Let p and x,|x|<1 be given. We wish to show that


where pn¯ denotes the nth falling factorial of p.

The convergence of the series in the right-hand side of the above equation is a straight-forward consequence of the ratio testMathworldPlanetmath. Set


and note that


The desired equality now follows from Taylor’s Theorem. Q.E.D.

Title proof of binomial formula
Canonical name ProofOfBinomialFormula
Date of creation 2013-03-22 12:24:00
Last modified on 2013-03-22 12:24:00
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 6
Author rmilson (146)
Entry type Proof
Classification msc 26A06