Find an approximation of $(0.99)^{5}$ using the first three terms of its expansion.

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Solution

We have $(0.99)^{5} = (1 - 0.01)^{5}$

$= 5_{C_{0}} - 5_{C_{1}} (0.01) - 5_{C_{2}} (0.01)^{2} . . .$

$= 1 - (5 \times 0.001) + (10 \times 0.0001) . . .$

$= 1 - 0.05 + 0.001 . . . = 0.951$

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