Difference between revisions of "Triangular numbers"
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| − | The triangular numbers $T(n)$ are defined by the formula | + | The triangular numbers $T(n)$ are defined for $n=1,2,3,\ldots$ by the formula |
$$T(n)=\displaystyle\sum_{k=1}^n k.$$ | $$T(n)=\displaystyle\sum_{k=1}^n k.$$ | ||
They represent the number of ways to draw an equilateral triangle as in the image below. | They represent the number of ways to draw an equilateral triangle as in the image below. | ||
Revision as of 01:24, 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))
