mathematics

==== You have won and amazing competition! ==== ==== On a chess board you get to put 1cent on the first square,2 on the next, 4 on the next, 8 on the next, 16...all the way to 64. ==== ==== You get to keep all the money! ==== ==== For Example : after the 3rd square you get to keep 1 plus 2 plus, 4=7 cents. ==== ==== How much would you score in total 'loot'? ==== ==== Is it possible to find out a formula to solve this. ====

775808 || 4611686018427 387904 || 230584300921 3693952 || 1152921504606 846976 || 5764607523034 23488 || 2882303761517 11744 || 1441151880758 55872 || 72057594037 927936 || 710656 || 562949953 421312 || 1125899906 842624 || 2251799813 685248 || 4503599627 370496 || 9007199254 740992 || 18014398509 481984 || 36028797018 963968 || 355328 || 70368744 177664 || 35184372 088832 || 17592186 044416 || 8796093 022208 || 4398046 511104 || 2199023 255552 || 1099511 627776 ||
 * 9223372036854
 * 281474976
 * 140737488
 * 4294967296 || 8589934592 || 17179869184 || 34359738368 || 68719476 || 137438953472 || 274877906944 || 549755813888 ||
 * 2147483648 || 1073741824 || 536870912 || 268435456 || 134217728 || 67108864 || 33554432 || 16777216 ||
 * 65536 || 131072 || 262144 || 524288 || 1048576 || 2097152 || 4194304 || 8388608 ||
 * 32768 || 16384 || 8192 || 4096 || 2048 || 1024 || 512 || 256 ||
 * 1 || 2 || 4 || 8 || 16 || 32 || 64 || 128 ||