1 + 2 + 4 + 8 + ⋯ that and , but the underlying proofs demand careful thinking about the interpretation of endless sums. It is also possible to view this series as convergent in a number system different from the real numbers, namely, the 2-adic numbers. As a series of 2-adic numbers this series converges to the same sum, −1, as was derived above by analytic continuation. 1 + 2 + 4 + 8 + ⋯ In mathematics, is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2.
How Many Miles to Babylon? How Many Miles to Babylon? "How Many Miles to Babylon" is an English language nursery rhyme. It has a Roud Folk Song Index number of 8148. The accepted modern lyrics are: <poem>How many miles to Babylon? Three score miles and ten. Can I get there by candle-light? Yes, and back again.. If your heels are nimble and your toes are light, You may get there by candle-light.</poem> A longer Scottish version has the lyrics: <poem>King and Queen of Cantelon, How many miles to Babylon? Eight and eight, and other eight. Will I get there by candle-light? If your horse be