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Ifthecoefficientsofx ^(9), x ^( 10) , x ^ ( 11 )intheexpansion of(1 +x ) ^nareinarithmeticprogressionthenn^ 2-41 n= |
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Answer» `398` `therefore""^n c _9,""^n c _ (10),""^nc _(11)` arein `A.P` `therefore2 (nc _ (10)) =nc _ 9 +nc _ (11)` ` rArr2= (nc _9 ) /(nc _ (10))+(nc _(11))/(nc _ (10)) ` ` rArr 2= (10)/(n - 10+1 ) +(n - 11+ 1 )/(11)[ because(nc _r )/(nc _ (R - 1 ))= (n -r + 1 )/(r ) ] ` ` rArr 2=(10)/(n - 9)+(n - 10)/(11)` `rArr2-(10)/(n-9 )=(n -10)/(11)` ` rArr(2n -28)/(n -9 ) = (n -10)/(11)` ` rArr11 (2n- 28) =(n - 9 )(n - 10) ` `rArr22n- 308=n ^ 2-19n +90 ` `thereforen^ 2 - 41 n+398=0 ` |
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