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Question
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
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Solution
By splitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)10000 can be obtained as
(1.1)10000 = (1 + 0.1)10000
= `1^10000 + 10000C_1 xx 1^9999 (0.1)^1`
= 1 + 10000 x (0.1) + …. = 1001 +…
It is clear that the number (1.1)10000 is greater than 1000.
Hence, (1.1)10000 > 1000
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