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29. The given sum is equal to (m₂ + my + ms). 2+m³). n To see this, compute the coefficient of " in each side of (1+x)(1+x)(1+x)m³ = (1+x)m₁+m₂+ms In this computation use the binomial theorem.

29. The given sum is equal to (m₂ + my + ms). 2+m³). n To see this, compute the coefficient of " in each side of (1+x)(1+x)(1+x)m³ = (1+x)m₁+m₂+ms In this computation use the binomial theorem.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find and prove a formula for Σ r, s, t > 0 r+s+t=n (™¹) (m²) (m³), where the summation extends over all nonnegative integers r, s and t with sum r+s+t=n.
Transcribed Image Text:Find and prove a formula for Σ r, s, t > 0 r+s+t=n (™¹) (m²) (m³), where the summation extends over all nonnegative integers r, s and t with sum r+s+t=n.
29. The given sum is equal to m₂ + m₂ + Mz + m²). To see this, compute the coefficient of an in each side of n (1+x)(1+x)² (1+x)m³ = (1+x)m₁+m₂+m³ In this computation use the binomial theorem.
Transcribed Image Text:29. The given sum is equal to m₂ + m₂ + Mz + m²). To see this, compute the coefficient of an in each side of n (1+x)(1+x)² (1+x)m³ = (1+x)m₁+m₂+m³ In this computation use the binomial theorem.
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