1. Pure Mathematics 1

Binomial Expansion — Quiz

Test your understanding of binomial expansion with 5 practice questions.

Practice Questions

Question 1

In the binomial expansion of $(1+x)^n$, the ratio of consecutive coefficients $C(n,k+1)$ to $C(n,k)$ simplifies to which expression?

Question 2

What is the coefficient of $x^3$ in the expansion of $(3+2x)^{-4}$?

Question 3

Using the first three terms of the binomial expansion of $(1 - x)^{-\tfrac{3}{2}}$, what is the approximate value of $(0.96)^{-\tfrac{3}{2}}$?

Question 4

What are the first three non-zero terms in ascending powers of $x$ in the binomial expansion of $(5+x)^{\tfrac{3}{2}}$?

Question 5

Why does the binomial expansion of $(1+x)^n$ terminate after a finite number of terms when $n$ is a non-negative integer?