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Question-4584




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

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