Evaluate the following: (0.99)^5+(1.01)^5 - Vidyadip

Question

Evaluate the following:

$(0.99)^5+(1.01)^5$

✓

Answer

$(0.99)^5+(1.01)^5$

$=(1-.01)^5+(1+.01)^5$

$=2\big[{^5\text{C}}_1+{^5\text{C}}_3(.01)^2+{^5\text{C}}_5(.01)^5\big]$

$=2\Big[5+10\times\frac{1}{10^4}+\frac{1}{10^{10}}\Big]$

$=2\Big[5+\frac{1}{1000}+\frac{1}{10^{10}}\Big]$

$=2.0020001$

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