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Largest term in the (a+b)^n expansion

Source: 1st German pre-TST 2005, 6 Dec 2004, Problem 1

December 15, 2004

inequalitiesalgebra proposedalgebra

Problem Statement

Given the positive numbers

a

and

b

and the natural number

n

, find the greatest among the

n + 1

monomials in the binomial expansion of

\left(a+b\right)^n