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Reverse of Summation

 
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sgaznwang
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Joined: 18 Nov 2003
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PostPosted: Tue, 18 Nov 2003 00:26:12 UTC    Post subject: Reverse of Summation Reply with quote
Hey.. I have a question on how to find the reverse of a summation equation. For example, I have
a=Summation from i=1 to N of (m/[(i-j)^2+h^2]).
With j and h held constant, I want to find what m=.
N is just a number picked at random so i changes with the summation as it goes from 1 to N.
Any help would be appreciated thanks!
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Soroban
Member of the 'S.O.S. Math' Hall of Fame


Joined: 19 May 2003
Posts: 7246
Location: Lexington, MA
PostPosted: Tue, 18 Nov 2003 01:57:28 UTC    Post subject: Re: Reverse of Summation Reply with quote
Hello, sqaznwang!

Quote:
Hey.. I have a question on how to find the reverse of a summation equation.

For example, I have:

With j and h held constant, I want to find what m=.
N is just a number picked at random so ii changes with the summation as it goes from 1 to N.

This particular problem is simple. (Others may not be as easy.)

Since i is the only variable, then m is also a constant.
It can be factored out of the summation.

So:

Then solve for m:
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