The statement that 1 / 2 − 1 / 4 1 / 8 − 1 / 16 ⋯ is absolutely convergent means that the series 1 / 2 1 / 4 1 / 8 1 / 16 ⋯ is convergent In fact, the latter series converges to 1, and it proves that one of the binary expansions of 1 is 0111 Now, we add the numerators of 6/8 and 1/8 6 1 = 7, which means that 3/4 1/8 = 7/8 Thus, by first adding 1/2 plus 1/4 and then adding 1/8 to the result, we find that 1/2However, lists are not efficient for this purpose
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