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Questions and Answers
If the sum of the coefficients of all even powers of $x$ in the product is 61, what is the value of $n$?
If the sum of the coefficients of all even powers of $x$ in the product is 61, what is the value of $n$?
- 8 (correct)
- 9
- 10
- 7
What is the sum of the coefficients of all even powers of $x$ in the product $(1 + x + x^2 + … + x^{2n}) (1 – x + x^2 – x^3 + … + x^{2n})$?
What is the sum of the coefficients of all even powers of $x$ in the product $(1 + x + x^2 + … + x^{2n}) (1 – x + x^2 – x^3 + … + x^{2n})$?
- $n^2$
- $2n^2 - 1$ (correct)
- $2n^2 + 1$
- 2n + 1
What is the coefficient of $x^{10}$ in the product $(1 + x + x^2 + … + x^{20}) (1 – x + x^2 – x^3 + … + x^{20})$?
What is the coefficient of $x^{10}$ in the product $(1 + x + x^2 + … + x^{20}) (1 – x + x^2 – x^3 + … + x^{20})$?
- -19 (correct)
- -17
- -16
- -18
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