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From: hes@ecsvax.UUCP
Newsgroups: net.math
Subject: Re: series sum
Message-ID: <1118@ecsvax.UUCP>
Date: Fri, 24-Jan-86 10:45:31 EST
Article-I.D.: ecsvax.1118
Posted: Fri Jan 24 10:45:31 1986
Date-Received: Sat, 25-Jan-86 09:27:57 EST
References: <2265@utcsstat.uucp>
Organization: NC State Univ.
Lines: 21

> 
> 	Can anyone deduce the sum of the following series after n terms?
> 
> 	  1 + 3 + 6 + 10 + 15 + 21 + .....
> -- 
>        	{allegra,ihnp4,linus,decvax}!utzoo!utcsstat!anthony
  This appears to be (using S for capital sigma):

        n      k
        S      S  i
       k=1    i=1

The second summation = k(k+1)/2, and then the first summation can be
performed by multiplying this out, separating the terms, using this same
relationship again plus this one:

        n
        S    k^2   =  n(n+1)(2n+1)/6
       k=1

--henry schaffer