Difference between revisions of "Triangular numbers"
From specialfunctionswiki
| Line 13: | Line 13: | ||
[[T(n+1)=T(n)+n+1]]<br /> | [[T(n+1)=T(n)+n+1]]<br /> | ||
[[n^2=T(n)+T(n-1)]]<br /> | [[n^2=T(n)+T(n-1)]]<br /> | ||
| − | [[T(n)^2=T(T(n))+T(T(n-1 | + | [[T(n)^2=T(T(n))+T(T(n)-1)]]<br /> |
=References= | =References= | ||
Revision as of 01:26, 30 May 2017
The triangular numbers $T(n)$ are defined for $n=1,2,3,\ldots$ by the formula $$T(n)=\displaystyle\sum_{k=1}^n k.$$ They represent the number of ways to draw an equilateral triangle as in the image below.
Graphical representation of the first six triangular numbers.
Properties
T(n)=n(n+1)/2
T(n+1)=T(n)+n+1
n^2=T(n)+T(n-1)
T(n)^2=T(T(n))+T(T(n)-1)
