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Question
Using binomial theorem determine which number is larger (1.2)4000 or 800?
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Solution
We have:
(1.2)4000
\[= (1 + 0 . 2 )^{4000} \]
\[ = ^{4000}{}{C}_0 + ^{4000}{}{C}_1 \times (0 . 2 )^1 + ^{4000}{}{C}_2 \times (0 . 2 )^2 + . . . ^{4000}{}{C}_{4000} \times (0 . 2 )^{4000}\]
\[= 1 + 4000 \times 0 . 2 + \text{ other positive terms} \]
\[ = 1 + 800 + \text{ other positive terms } \]
\[ = 801 + \text{ other positive terms} \]
\[ \because 801 > 800\]
Hence, (1.2)4000 is greater than 800
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