# Using Binomial Theorem, indicate which number is larger (1.1)^10000 or 1000.

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Using Binomial Theorem, indicate which number is larger (1.1)^10000 or 1000.

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Solution:

Splitting 1.1 and using Binomial Theorem to write the first few terms we have

(1.1)10000 = (1+0.1)10000
= 10000C0 + 10000C1(0.1) +10000C2(0.1)2 + other positive terms.
= 1 + 10000 ´ (0.1) + other positive terms
= 1 + 1000 + other positive terms
>1000
Hence, (1.1)10000 > 1000.