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

Q7. Find an approximation of (0.99)5 using the first three terms of its expansion.

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As we can write 0.99 as 1-0.01,

(0.99)^5=(1-0.001)^5=^5C_0(1)^5-^5C_1(1)^4(0.01)+^5C_2(1)^3(0.01)^2+\:other \:negligible \:terms

\Rightarrow (0.99)^5=1-5(0.01)+10(0.01)^2

\Rightarrow (0.99)^5=1-0.05+0.001

\Rightarrow (0.99)^5=0.951

Hence the value of   (0.99)^5  is 0.951 approximately.

Posted by

Pankaj Sanodiya

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