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

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

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3 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 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
23 Points
9 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
40 Points
9 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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