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If the coefficient of $(2r+4)^{th}$ and $(r-2)^{th}$ terms in the expansion of $(1+x)^{18} $ are equal, then $r=?$

$\begin{array}{1 1} 5 \\ 6 \\ 7 \\ No\;r\;exists \end{array}$

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In the expansion of $(1+x)^{18}$,
Coefficient of $T_{2r+4}=^{18}C_{2r+3}$
Coefficient of $T_{r-2}=^{18}C_{r-3}$
Given: $^{18}C_{2r+3}=^{18}C_{r-3}$
$\Rightarrow\:2r+3=r-3\:\:or\:2r+3=18-r+3=21-r$
$\Rightarrow\:r=-6\:\:or\:\:3r=18$
Since $r$ cannot be - ve , $r=6$
answered Sep 24, 2013 by rvidyagovindarajan_1
 

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