Find the first four terms of $(1-2x)^5$ in ascending powers of $x$. Hence estimate $0.98^5$ to

Question

Find the first four terms of $(1-2x)^5$ in ascending powers of $x$. Hence estimate $0.98^5$ to three decimal places. Calculate the omitted terms at the chosen $x$, and verify your rounding.

Accepted Answer

(a) $1-10x+40x^2-80x^3$; (b) $0.904$; (c) Omitted total $0.0000007968$.

Binomial Theorem

Binomial Theorem