Difference between revisions of "T(n)=n(n+1)/2"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds for all $n=1,2,3,\ldots$: $$T(n)=\dfrac{n(n+1)}{2},$$ where $T$ denotes triangular numbers. ==Proof== ==References== * {{PaperRef...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
The following formula holds for all $n=1,2,3,\ldots$: | The following formula holds for all $n=1,2,3,\ldots$: | ||
$$T(n)=\dfrac{n(n+1)}{2},$$ | $$T(n)=\dfrac{n(n+1)}{2},$$ | ||
| − | where $T$ denotes [[triangular numbers]]. | + | where $T(n)$ denotes the $n$th [[triangular numbers|triangular number]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| − | * {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=Triangular numbers|next=T(n+1)=T(n)+n+1}} | + | * {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=Triangular numbers|next=T(n+1)=T(n)+n+1}} $(1.1)$ |
Latest revision as of 01:28, 30 May 2017
Theorem
The following formula holds for all $n=1,2,3,\ldots$: $$T(n)=\dfrac{n(n+1)}{2},$$ where $T(n)$ denotes the $n$th triangular number.
Proof
References
- V.E. Hoggatt, Jr and Marjorie Bicknell: Triangular numbers (1974)... (previous)... (next) $(1.1)$
