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Solving a Complicated Equation


Date: 25 Apr 1995 01:34:40 -0400
From: Anonymous
Subject: IMPORTANT

Dear Dr. Math:

I sent you a difficult math problem yesterday.  Here is that
problem again:
         Please solve this equation for variable X with parameter k:  
               sin(X)+sin(5*X)+sin(9*x)+....+sin((4*k+1)*X)=k+1
My internet address has been changed. Please send the answer
to this address:
            malayeri@ece.ut.ac.ir 
Thank you.
   reza navid               


Date: 28 Apr 1995 15:33:39 -0400
From: Dr. Ken
Subject: Re: IMPORTANT

Hello there!

Here's something to think about in that equation: there are k+1 terms on the
left side of the equation (one for each value that goes from 0 to k), each
of which is less than or equal to 1.  The right side is k+1.  What
constraints must be put on k+1 numbers, each of which is less than or equal
to 1, so that they add up to k+1?

Once you've got that, see if the rest of the problem falls into place.  If
you still have trouble, write us back and we'll give you some more hints.

-K
    
Associated Topics:
High School Basic Algebra

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