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From: stark@sbcs.UUCP (Eugene Stark)
Newsgroups: net.math
Subject: Re: series sum
Message-ID: <42@sbcs.UUCP>
Date: Mon, 27-Jan-86 10:00:45 EST
Article-I.D.: sbcs.42
Posted: Mon Jan 27 10:00:45 1986
Date-Received: Thu, 30-Jan-86 06:04:23 EST
References: <2265@utcsstat.uucp>
Organization: Computer Science Dept, SUNY@Stony Brook
Lines: 34

> 
> 	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
>         {ihnp4|decvax|utzoo|utcsrgv}!utcs!utzoo!utcsstat!anthony

Assuming that you want the sum of the first n triangular numbers:

		n   i
		--  --
		\   \
		/   /   j	=	n(n+1)(n+2)/6
		--  --
		i=1 j=1

You can derive this yourself if you use the fact that the sum

		n
		--
		\   k
		/  i
		--
		i=1

is a polynomial in n of order k+1.  Or, you can look up in a book
the sums for k = 1 and k = 2, namely n(n+1)/2 and n(n+1)(2n+1)/6.


					Gene Stark
					SUNY at Stony Brook