Use the method of direct proof to prove the following statement. If n ∈ N, then n^2 = 2 (n 2) + (n 1). (You may need a separate case for n = 1.) Note: (n 2) means n choose 2, (n 1) means n choose 1.
Use the method of direct proof to prove the following statement. If n ∈ N, then n^2 = 2 (n 2) + (n 1). (You may need a separate case for n = 1.) Note: (n 2) means n choose 2, (n 1) means n choose 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 14E
Question
Use the method of direct proof to prove the following statement.
If n ∈ N, then n^2 = 2 (n 2) + (n 1). (You may need a separate case for n = 1.)
Note: (n 2) means n choose 2, (n 1) means n choose 1.
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