Theory question 103
Binomial Theorem(a) Write down the binomial expansion of (2 − x)5 in ascending powers of x.
(b) Use your expansion in 3(a) to evaluate (1.98)5 correct to four decimal places.
Show the model answer
Model answer
(a) (2 − x)5 = 32 − 80x + 80x2 − 40x3 + 10x4 − x5
(b) 1.98 = 2 − 0.02, so x = 0.02
32 − 1.6 + 0.032 − 0.00032 + 0.0000016 − ... = 30.43168
(1.98)5 ≈ 30.4317 (4 d.p.)
Explanation
Choose x so that 2 − x = 1.98, i.e. x = 0.02 (not 0.2).