Question

Find an approximation of `(0. 99)^5` using the first three terms of its expansion.

Answer 1

`0.99 = 1 - 0.01`
`:. (0.999)^(5) = (1-0.01)^(5)`
`= .^(5)C_(0)(1)^(5) - .^(5)C_(1) (1)^(4) - (-0.01) + .^(5)C_(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`.