Multimagic square 16, 25, 36, 49, ... Sum of Squares 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... )number of units in a square-based pyramid) The bimagic series is the 1st, 4th, 9th in this series (divided by 1, 2, 3, n) etc. so values for the rows and columns in order-1, order-2, order-3 Bimagic squares would be 1, 15, 95, 374, 1105, 2701, 5775, 11180, ... The trimagic series would be related in the same way to the hyper-pyramidal sequence of nested cubes. Cubes 0, 1, 8, 27, 64, 125, 216, ... Sum of Cubes 0, 1, 9,
1/4 + 1/16 + 1/64 + 1/256 + ⋯ sum of an infinite series is defined as the limit of its partial sums, 1/4 + 1/16 + 1/64 + 1/256 + ⋯ In mathematics, the infinite series is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. As it is a geometric series with first term and common ratio , its sum is The series lends itself to some particularly simple visual demonstrations because a square and a triangle both divide into four similar pieces, each of which contains the area of the