Sum of consecutive (triangular) cubes (Nicomachus's theorem)
Description
In number theory, the sum of the first n cubes is the square of the nth triangular number. The sequence of squared triangular numbers is
0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, ... (sequence A000537 in OEIS).These numbers can be viewed as figurate numbers, a four-dimensional hyperpyramidal generalization of the triangular numbers and square pyramidal numbers.
Related formulasVariables
| S | Sum of consecutive cubes (dimensionless) |
| n | Nth term (dimensionless) |