Triangular numbers

From specialfunctionswiki
Revision as of 01:17, 30 May 2017 by Tom (talk | contribs)
Jump to: navigation, search

The triangular numbers $T(n)$ are defined 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.

Properties

T(n) equals 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))

References

Polygonal numbers