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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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If x , y , z are in GP then , $\;\large\frac{1}{x^2-y^2}+\frac{1}{y^2}\;$ equals

$(a)\;\large\frac{1}{z^2-y^2}\qquad(b)\;\large\frac{1}{y^2-z^2}\qquad(c)\;\large\frac{1}{z^2-x^2}\qquad(d)\;\large\frac{1}{y^2-x^2}$

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Answer : (b) $\;\large\frac{1}{y^2-z^2}$
Explanation : $\;\large\frac{1}{x^2-y^2}+\frac{1}{y^2}$
$=\frac{1}{x^2}(\large\frac{1}{1-r^2}+\frac{1}{r^2})$
$=\frac{1}{x^2}(\frac{1}{r^2}*\large\frac{1}{1-r^2})$
$=\large\frac{1}{y^2-z^2}\;.$
answered Jan 22, 2014 by yamini.v
 

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