3 Questions
If the sum of the coefficients of all even powers of $x$ in the product is 61, what is the value of $n$?
8
What is the sum of the coefficients of all even powers of $x$ in the product $(1 + x + x^2 + … + x^{2n}) (1 – x + x^2 – x^3 + … + x^{2n})$?
$2n^2 - 1$
What is the coefficient of $x^{10}$ in the product $(1 + x + x^2 + … + x^{20}) (1 – x + x^2 – x^3 + … + x^{20})$?
-19
Solve for the value of n in the given polynomial product where the sum of the coefficients of all even powers of x is known to be 61. The expression involves expanding and multiplying polynomial terms.
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