CALCULATOR
Triangular Number for a Selected Positive Index Calculator
Triangular Number for a Selected Positive Index. Positive index: 1, 2, 3, 5, 10, 50, 100, 1000 only. Example: Positive index: 10 count gives 55 count. Index selected from1,2,3,5,10,50,100,1000; dimensionless count, no arbitrary fractional index. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Index selected from1,2,3,5,10,50,100,1000; dimensionless count, no arbitrary fractional index. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Pair ascending and descending sum1+...+n, producing n pairs of n+1.
Accepted inputs: Positive index: choose 1 (1), 2 (2), 3 (3), 5 (5), 10 (10), 50 (50), 100 (100), 1000 (1000).
How the calculation works
T_n=n(n+1)/2
Worked example
With positive index 10, triangular number for a selected positive index is 55 count.
Assumptions and limits
Index selected from1,2,3,5,10,50,100,1000; dimensionless count, no arbitrary fractional index. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Pair ascending and descending sum1+...+n, producing n pairs of n+1.