2.7: Binomial coefficients and approximation

In the binomial expansion of $\left(a - \tfrac{x}{2}\right)^{6}$, the coefficient of $x^{3}$ is 120 times the coefficient of $x^{5}$. Find the possible values of the constant $a$.

Expand $(1 + 2x)^{20}$ in ascending powers of $x$, as far as the term in $x^{3}$. Simplify each term.

Use your expansion to show that the value of $0.98^{20}$ is $0.67$ to 2 decimal places.