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Algebra> how to find coefficient of x^n in 1/(1-x)...

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how to find coefficient ofx^nin 1/(1-x)(1-2x)(1-3x)ans is ( 3^n+2-2^n+3+1)/2 sir pl explain the method

man , 10 Years ago

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3 Answers

Nishant Vora

Last Activity: 10 Years ago

$=> \frac{1}{(1-x)(1-2x)(1-3x)} = (1-x)^{-1}(1-2x)^{-1}(1-3x)^{-1}$
$Now (1-x)^{-1} = 1 + x + x^2 + x^3 + .....x^{n}$
$Now (1-2x)^{-1} = 1 + 2x + 2x^2 + 2x^3 + .....2x^{n}$
$Now (1-3x)^{-1} = 1 + 3x + 3x^2 + 3x^3 + .....3x^{n}$

coefficient of x^n => Multiply the above and check x^n

man

Last Activity: 10 Years ago

thanhs to ans but i think its not easy to observe how will we explain to find coefficient by multiplication to a student sir

abhishek singh

Last Activity: 10 Years ago

in these kind of questions u can only multiply the coefficents , same kind of question came this year in iit advance paper 1,, integer type

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