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 + ⋯ is that the partial sums of the series are: This form can be proved by multiplying both sides by 1 − and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs. The same strategy works for any finite geometric series. Archimedes' Proposition 24 applies the finite (but indeterminate) sum in Proposition 23 to the area inside a parabola by a double "reductio ad absurdum". He does not "quite" take the limit of the above partial sums, but in modern calculus this step is easy enough: Since the