Difference between revisions of "Triangular number"
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Using the sum of an [[arithmetic series]] formula, a formula can be calculated for <math>\displaystyle T_n</math>: | Using the sum of an [[arithmetic series]] formula, a formula can be calculated for <math>\displaystyle T_n</math>: | ||
− | :<math>T_n = \displaystyle\sum_{ | + | :<math>T_n = \displaystyle\sum_{k=1}^{n}k = 1 + 2 + \ldots + n = \frac{n(n+1)}2</math> |
− | The rather simple recursive definition can be easily found by noting that <math>\displaystyle T_{n} = 1 + 2 \ | + | The rather simple recursive definition can be easily found by noting that <math>\displaystyle T_{n} = 1 + 2 + \ldots + (n-1) + n = (1 + 2 + \ldots + n-1) + n = T_{n-1} + n</math>. |
{{stub}} | {{stub}} |
Revision as of 03:11, 8 September 2007
The triangular numbers are the numbers which are the sum of the first natural numbers from to .
Using the sum of an arithmetic series formula, a formula can be calculated for :
The rather simple recursive definition can be easily found by noting that .
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