Q6. Let n be n₁ + N₂ + N3 +・・・+nt, where each n; is a positive integer. Use the definition of binomial coefficients to prove that n₁ + n1 + nt -1₁) (1²₂ + nt ) (ns + ... + ₁) ... (1²) (1² = n3 n₂ + ... + nt n2 n! nt n₁!n₂!...nt!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 26E
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Q6. Let n be n₁ + N₂ + N3+ +nt, where each n, is a positive integer. Use the definition of
binomial coefficients to prove that
nt
+
(m₁ + ... + m²) (₂².
n1
N2
nt
+ nt
m²) (13 + m₂ + m²)....(m)
nt
n3
=
n!
'n₁!n₂! ne!"
Transcribed Image Text:Q6. Let n be n₁ + N₂ + N3+ +nt, where each n, is a positive integer. Use the definition of binomial coefficients to prove that nt + (m₁ + ... + m²) (₂². n1 N2 nt + nt m²) (13 + m₂ + m²)....(m) nt n3 = n! 'n₁!n₂! ne!"
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