Difference between revisions of "Triangular numbers"

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(Properties)
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=Properties=
 
=Properties=
[[T(n)= n(n+1)/2]]<br >
+
[[T(n)=n(n+1)/2]]<br >
 
[[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 />

Revision as of 01:22, 30 May 2017

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)=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