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Question
Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
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Solution
\[(1 . 01 )^{10} + (1 - 0 . 01 )^{10} \]
\[ = (1 + 0 . 01 )^{10} + (1 - 0 . 01 )^{10} \]
\[ = 2[ ^{10}{}{C}_0 \times (0 . 01 )^0 +^{10}{}{C}_2 \times (0 . 01 )^2 +^{10}{}{C}_4 \times (0 . 01 )^4 +^{10}{}{C}_6 \times (0 . 01 )^6 + ^{10}{}{C}_8 \times (0 . 01 )^8 + ^{10}{}{C}_{10} \times (0 . 01 )^{10} ]\]
\[ = 2\left( 1 + 45 \times 0 . 0001 + 210 \times 0 . 00000001 + . . . \right) \]
\[ = 2\left( 1 + 0 . 0045 + 0 . 00000210 + . . . \right)\]
\[ = 2 . 0090042 + . . .\]
Hence, the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of the decimal is 2.0090042
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