Emerald Tablets Of Thoth, 50,000 Year Old Tablets Reportedly From Atlantis have been found

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 =
32/64 + 16/64 + 8/64 + 4/64 + 2 /64 + 1/64 = 63/64

So, where is the missing 1/64 ???

1/2 + 1/4 + 1/8 + 1/16 + ⋯


First six summands drawn as portions of a square.

In mathematics, the infinite series 1/2 + 1/4 + 1/8 + 1/16 + · · ·
is an elementary example of a geometric series that converges absolutely.

Its sum is

Direct proof

As with any infinite series, the infinite sum

is defined to mean the limit of the sum of the first n terms

as n approaches infinity. Multiplying s_n by 2 reveals a useful relationship:

Subtracting s_n from both sides,

As n approaches infinity, s_n tends to 1.

(see the hard to read parts at http://en.wikipedia.org/wiki/1/2_+_1/4_+_1/8_+_1/16_+_⋯)