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Question Number 29310 by tawa tawa last updated on 07/Feb/18
Show that the sequence:     {1 + (1/2) + (1/4) + ... + (1/2^n )}_(n  = 0) ^∞          is convergent.
$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}:\:\:\:\:\:\left\{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }\right\}_{\mathrm{n}\:\:=\:\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{convergent}. \\ $$

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