Question Number 4584 by MrGreg last updated on 08/Feb/16
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Answered by FilupSmith last updated on 09/Feb/16
$$\:\:\:\:{S}=\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$+{S}=\mathrm{0}+\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$\mathrm{2}{S}=\mathrm{1}+\left(−\mathrm{1}+\mathrm{2}−\mathrm{4}+\mathrm{8}−\mathrm{16}+…\right) \\ $$$$\mathrm{2}{S}=\mathrm{1}−{S} \\ $$$$\therefore{S}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$