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       #Post#: 118--------------------------------------------------
       EULERS IDENTITY
       By: eba95 Date: July 30, 2010, 6:52 am
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       Euler's Identity
       Here is an amazing formula due to
       Euler:
       SUMn=1 to infinity n-s = PRODp prime
       (1 - p-s)-1 .
       What's interesting about this
       formula is that it relates an
       expression involving all the positive
       integers to one involving just
       primes!
       Presentation Suggestions:
       Interested students may wish to take
       a few terms on the right hand side,
       use a power expansion, and multiply
       them out... to get an idea of why the
       equality holds.
       The Math Behind the Fact:
       The left hand side, when s is viewed
       as a complex variable, is also known
       as the Riemann zeta function.
       Because of the above relationship,
       the study of zeta functions is closely
       related to the study of the
       distribution of primes!
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