Sequence of Triangular NumbersDate: 13 Jul 1995 09:46:53 -0400 From: richard rudolph Subject:Sequence What is this sequence called: 1,3,6,10,15 How is it generated? Richard Rudolph :-) Date: 13 Jul 1995 22:39:00 -0400 From: Dr. Ken Subject: Re: Sequence Hello there! This sequence is called the sequence of Triangular Numbers. It's called that for the following reason: * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . . . . (count the stars) Notice that if you count the number of stars in a triangle by counting the number of stars in each row and then adding them, you'll get something like this (this is for the last triangle): 1+2+3+4+5+6 = 21. In general, if you add up the first n positive integers, you'll get the number n(n+1)/2. Do you see why? If you want to know why, you can write back to us (but try to figure it out for yourself first, it's pretty neat!). Thanks for the question! -K |
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