11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?

11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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