Determine Parameters from Conditions on Coefficients or Terms
The question provides conditions on coefficients or terms (e.g., sum of coefficients equals zero, coefficients in AP/GP, a ratio between specific coefficients) and asks to find unknown parameters such as n, a, m/n, or r.
Let $m$ and $n$ be natural numbers. If the constant term in the expansion of $$\left(x + \frac{5}{x^{m}}\right)^{n}$$ is 60, what is $m + n$? A) 36 B) 35 C) 31 D) 27 E) 23
Let $n$ be a positive integer. In the expansion of $$\left(x^{2} + x\right)^{n}$$ both the coefficient of the term containing $x^{19-n}$ and the coefficient of the term containing $x^{16-n}$ equal a positive integer $k$. Accordingly, what is $k$? A) 6 B) 12 C) 15 D) 18 E) 21