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From: lew@ihuxr.UUCP
Newsgroups: net.math
Subject: An interesting identity
Message-ID: <532@ihuxr.UUCP>
Date: Thu, 4-Aug-83 13:06:43 EDT
Article-I.D.: ihuxr.532
Posted: Thu Aug  4 13:06:43 1983
Date-Received: Sat, 6-Aug-83 08:51:34 EDT
Organization: BTL Naperville, Il.
Lines: 22

I stumbled across the following identity:

	sum i=1 to n of (-1)^(i+1) * C(n,i) * 1/i

		equals

	sum i=1 to n of 1/i

Can anybody provide a reference for this, or show its equivalence to
some basic identity? Surely Euler knew this!

When I tried to prove it inductively by taking S(n+1) - S(n), I got

	sum i=1 to n of (-1)^(i+1) * C(n,i) * 1/(n+1-i)

		equals

	0, n even ; 2/(n+1), n odd

... so this doesn't really help.

	Lew Mammel, Jr. ihuxr!lew