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Question
Evaluate the
(viii) \[\left( 0 . 99 \right)^5 + \left( 1 . 01 \right)^5\]
Solution
\[(0 . 99 )^5 + (1 . 01 )^5 \]
\[ = (1 - 0 . 01 )^5 + (1 + 0 . 01 )^5 \]
\[ = 2[ ^{5}{}{C}_0 (0 . 01 )^0 + ^{5}{}{C}_2 (0 . 01 )^2 + ^{5}{}{C}_4 (0 . 01 )^4 ]\]
\[ = 2[1 + 10 \times 0 . 0001 + 5 \times 0 . 00000001]\]
\[ = 2 \times 1 . 00100005 = 2 . 0020001\]
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