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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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If x, y, z > 1 are in GP, then $\frac{1}{1+lnx}$, $\frac{1}{lny}$, $\frac{1}{lnz}$ are in

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None$

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Answer : (c) HP
Explanation : x , y , z in GP
$y^2=xz$
$ln\;y^2\;=\;ln\;xz$
$2\;ln\;y=ln\;x+ln\;z$
$ln\;x\;,ln\;y\;,ln\;z\;are\;in\;AP$
$1+ln\;x\;,1+ln\;y\;,1+ln\;z\;are\;in\;AP$
$\frac{1}{1+lnx}\;,\frac{1}{1+lny}\;,\frac{1}{1+lnz}\;are\;in\;HP.$
answered Jan 20, 2014 by yamini.v
 

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