4. Prove that for all n E N η Σ( r=0 = = (3) Hint: Examine the coefficient of x² by expanding both sides of the equality (1 + x)2n = (1 + x)" (1 + x)" = Use the definition of Binomial Identity.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 50E
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XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
4. Prove that for all n E N
n
2
2n
Σ (²)² = (²n)
r=0
XXXXXXXXXX
Hint: Examine the coefficient of x¹ by expanding both sides of the equality
(1 + x)²n = (1 + x)” (1 + x)n
Use the definition of Binomial Identity.
Transcribed Image Text:Solve step by step in digital format XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 4. Prove that for all n E N n 2 2n Σ (²)² = (²n) r=0 XXXXXXXXXX Hint: Examine the coefficient of x¹ by expanding both sides of the equality (1 + x)²n = (1 + x)” (1 + x)n Use the definition of Binomial Identity.
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