Triangular NumbersDate: 08/23/2003 at 20:44:13 From: Cough Subject: Triangle numbers How do I show that the sum of any two consecutive triangular numbers is always a square number? I can't seem to show triangular numbers as an equation. 1+2=3 1+2+3=6 1+2+3+4=10 1+2+3+4+5=15 1+2+3+4+5+6=21 1+3=4=2^2 3+6=9=3^2 6+10=16=4^2 Date: 08/23/2003 at 23:37:24 From: Doctor Stephanie Subject: Re: Triangle numbers Hi there! One thing that might make this problem a lot easier for you is to remember the formula for triangular numbers. If you want to find the "nth" triangular number, the formula you would use would be: N(N+1) -------- = Nth triangular number 2 Now try to use the formula to find the "Nth" triangular number and the "N+1st" triangular number. Then try adding the two consecutive triangular numbers together and simplify, and I think you will find what you are looking for. If you need me to continue on the problem a little bit further, or if you need more explanation, feel free to email me back! - Doctor Stephanie, The Math Forum http://mathforum.org/dr.math/ |
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