Recall that for every non-negative integer n the factorial is defined as n! = 1·2... (n-1). n. In particular, 0! = 1 and n! = (n − 1)! - n for n ≥ 1. For every integer 0 ≤ k ≤n, we now define the binomial coefficient (2) as n k We moreover set = n! k!(n - k)!* = 0 if k>n> 0. Let 1 ≤ k ≤ n. Prove that (2) = (¹) + (2−¹).

Recall that for every non-negative integer n the factorial is defined as n! = 1·2... (n-1). n. In particular, 0! = 1 and n! = (n − 1)! - n for n ≥ 1. For every integer 0 ≤ k ≤n, we now define the binomial coefficient (2) as n k We moreover set = n! k!(n - k)!* = 0 if k>n> 0. Let 1 ≤ k ≤ n. Prove that (2) = (¹) + (2−¹).

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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