InterviewSolution
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InterviewSolution
| 1. |
Find the coefficient of `x^(50)`in the expansion of `(1+x)^(101)xx(1-x+x^2)^(100)dot` |
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Answer» `(1+x)^(101)(1-x+x^(2))^(100)` `= (1+x)[(1+x)^(100) (1-x+x^(2))^(100)]` `= (1+x)(1-x^(3))^(100)` `= (1-x^(3))^(100) + x(1-x^(3))^(100)` `= (1-x^(3))^(100) + x(1-x^(3))^(100)` Now, coefficient of `x^(50)` in `[(1-x^(3))^(100) + x(1-x^(3))^(100)]` `=` Coefficient of `x^(50)` in `(1-x^(3))^(100)` + Coefficient of `x^(49)` in `(1-x^(3))^(100)` `= 0` (as 49 and 50 are not a multiple of 3) |
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