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the number of ways to write n = xı + · ··+ xm wit .. (a) Prove each of the following statements. i. Vn E Z+, P(1, n). ii. Vm e Z+, P(m, 1).

the number of ways to write n = xı + · ··+ xm wit .. (a) Prove each of the following statements. i. Vn E Z+, P(1, n). ii. Vm e Z+, P(m, 1).

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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Can you help me write down the induction proof for these two statements?

Induction. For m, n E Z*, define P(m, n) to be: (п + m - 1)! n!(m – 1)! the number of ways to write n = x1+ · · ·+ xm with x1,..., xm E N is - (a) Prove each of the following statements. i. Vn e Z+, P(1, n). ii. Vm e Z+, P(m, 1). 2.
Transcribed Image Text:Induction. For m, n E Z*, define P(m, n) to be: (п + m - 1)! n!(m – 1)! the number of ways to write n = x1+ · · ·+ xm with x1,..., xm E N is - (a) Prove each of the following statements. i. Vn e Z+, P(1, n). ii. Vm e Z+, P(m, 1). 2.
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