Multimagic square 36, 100, ... Value for Trimagic squares 1, 50, 675, 4624, ... Similarly the tetramagic sequence 4-Power 0, 1, 16, 81, 256, 625, 1296, ... Sum of 4-Power 0, 1, 17, 98, 354, 979, 2275, ... Sums for Tetramagic squares 0, 1, 177, ... The first known bimagic square has order 8 and magic constant 260 and a bimagic constant of 11180. It has been conjectured by Bensen and Jacoby that no nontrivial bimagic squares of order less than 8 exist. This was shown for magic squares containing the elements 1 to "n" by Boyer and Trump. However, J. R.
1/4 + 1/16 + 1/64 + 1/256 + ⋯ 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 original. In the figure on the left, if the large square is taken to