Question

Find an approximation of (0.99)5 using the first three terms of its expansion

Answer 1

$0.99 = 1 - 0.01$
$∴(0.99)^5 = (1-0.01)^5$
$=\space^5C_0 (1)^5 - \space^5C_1 (1)^4 (0.01) +\space ^5C_2 (1)^3 (0.01)^2$ (Approximately)
$=1-5(0.01)+10(0.01)^2$
$=1-0.05+0.001$
$=1.001-0.05$
$= 0.951$

Thus, the value of $(0.99)^5$ is approximately $0.951.$