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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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Sum of series $\;\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....\;is:$

$(a)\;\frac{n+1}{2^{n+1}}\qquad(b)\;\frac{n}{2^n}\qquad(c)\;n+1-\frac{1}{2^n}\qquad(d)\;n-1+\frac{1}{2^n}$

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1 Answer

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Answer : $\;{n-1+\frac{1}{2^n}}$
Explanation : $t_{r}=1-\frac{1}{2^r}$
$\sum_{r=1}^n\;(1-\frac{1}{2^r})=n-\frac{(1/2)\;(1-\frac{1}{2^n})}{1-\frac{1}{2}}$
$=n-1+\frac{1}{2^n}.$
answered Jan 20, 2014 by yamini.v
 

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