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Find the sum of the following series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots + \infty $

$(a)\;2\qquad(b)\;3\qquad(c)\;\frac{3}{2}\qquad(d)\;\infty$

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  • Sum of n terms of a GP is $S_{\infty} = \large \frac{a} {1 - r} $ when $ r < 1$
Sum of n terms of a GP is $S_{\infty} = \large \frac{a} {1 - r} $ when $ r < 1$
Here, $ a = 1, r = \frac {1}{2} $
$S_{\infty} = \Large\frac {1}{1 - \frac{1}{2}} $$= 2$
answered Nov 19, 2013 by harini.tutor
edited Jul 2, 2014 by balaji.thirumalai
 

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