InterviewSolution
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InterviewSolution
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The coefficient of `x^9` in the expansion of `(1 + x) (1 +x^2)(1 +x^3)...(1+x^(100))`isA. 2B. 6C. 9D. 8 |
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Answer» Correct Answer - d We observe that `x^(9)` can be formed in the following 8 ways : `x^(9+0), x^(1+8), x^(2 +7), x ^(3 +6), x^(4 +5), x^(1 + 3 + 5), x^(1 + 2 + 6), x ^(2 + 3 + 4)` and the coefficients in each case is 1. `therefore ` Coefficients of `x^(9) = underset(("8 - times"))(1 + 1 + ... + 1 = 8)` ALITER The coefficients of `x^(9)` is the number of ways in which the sum of the power of x is 9 as listed below. `x^(9) , x^(3) xxx^(8), x^(7), x^(3)xxx^(6), x^(4) xxx^(5), x^(1) xxx^(2)xxx^(6), x^(1) xxx^(3)xxx^(5),x^(2) xx^(3)xxx^(4)`. Clearly, these are 8 ways. |
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