Question

If \( (1 - x)^{10} = \sum_{r=0}^{10} a_r \, x^r (1 - x)^{30 - 2r} \), then find \( \frac{9a_9}{a_{10}} \).

Hint:

In complex binomial summations, always try to divide by a common power to create a single variable $y = f(x)$. This often reveals a simpler $(1+y)^n$ expansion.

Answer 1

Correct Answer: 21