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Find an approximation of (0. 99)^5using ...

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

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The correct Answer is:
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`(0.999)^(5)=(1-0.01)^(5)`
`=overset(5)underset(r=0)(Sigma).^(5)C_(r)(1)^(5-r)(0.01)^(r)`
`=overset(5)underset(r=0)(Sigma).^(5)C_(r)(-0.001)^(r)`
`=^(5)C_(0)(0.01)^(0-5)C_(1)(0.01)^(1)`
`+^(5)C_(2)(0.01)^(2)`
(Taking first three terms)
`=1-0.05+0.001`
`=0.951.`
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