The coefficients of x^50 in (1+x )^101(1-x+x^2)^100 is … … …

Question

Accepted Answer

Correct answer: C. (c) Given expression is (1+x )^101 (1-x+x )^100= (1+x )( (1+x )(1-x+x^2))^100= (1+x )(1+x^3)^100= coefficient of x^50 in (1+x )(1+x^3)^100= coefficient of x^50 in (1+x^3)^100+ coefficient of x^49 in (1+x^3)^100 In the expansion of (1+x^3)^100 In the expansion of (1+x^3)^100 Since 50 and 49 are not multiple of 3 . So, coefficient of x^50 and 49 in the expansion of (1+x^3)^100 is zero. Coefficient of x^50 in ( (1+x )^100(1-x+x^2))^101 is zero

$The coefficients of x^{50} in (1 + x)^{101} (1 - x + x^{2})^{100} is \dots \dots \dots$

Solution

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