number of terms in multinomial exapansion

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mutasimmim
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Joined: Sun Dec 12, 2010 10:46 am

number of terms in multinomial exapansion

Unread post by mutasimmim » Wed Sep 03, 2014 11:20 pm

Determine the number of terms in the expansion of $(a_1+a_2+a_3+....+a_n)^m$ where $m,n$ are positive integers.

Nirjhor
Posts: 136
Joined: Thu Aug 29, 2013 11:21 pm
Location: Varies.

Re: number of terms in multinomial exapansion

Unread post by Nirjhor » Thu Sep 04, 2014 12:32 am

HINT 1
The expansion is homogenous of degree \(m\).
HINT 2
The answer is \(\dbinom{m+n-1}{n-1}=\dbinom{m+n-1}{m}\).
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


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