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k It is known that ( + (₁ ²₁₂) + (k) = (²+¹) (k + 1). Prove that r - 2 (k) + ( k + ¹ ) + ( k + ²) + ... + (k+r) = (k+r+¹) k

k It is known that ( + (₁ ²₁₂) + (k) = (²+¹) (k + 1). Prove that r - 2 (k) + ( k + ¹ ) + ( k + ²) + ... + (k+r) = (k+r+¹) k

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.6: Binomial Theorem
Problem 45SE: In the expansion of (5x+3y)n , each term has the form (nk)ankbk ,where k successively takes on the...
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1. It is known that ² (₁₂ k ₁₂ ) + ( k) = (k + ¹) ( Prove that - r 2 (k) + (k + ¹) + (k + ²) + ... + (k + r) = (k+ + + ¹) k
Transcribed Image Text:1. It is known that ² (₁₂ k ₁₂ ) + ( k) = (k + ¹) ( Prove that - r 2 (k) + (k + ¹) + (k + ²) + ... + (k + r) = (k+ + + ¹) k
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