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Algebra

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

Profile image of man
11 Years agoGrade
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3 Answers

Profile image of Nishant Vora
11 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
Profile image of man
11 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
Profile image of abhishek singh
11 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