Question:
Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or 1000 .
Solution:
By splitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)10000 can be obtained as
$(1.1)^{10000}=(1+0.1)^{10000}$
$={ }^{10000} \mathrm{C}_{0}+{ }^{10000} \mathrm{C}_{1}(1.1)+$ Other positive terms
$=1+10000 \times 1.1+$ Other positive terms
$=1+11000+$ Other positive terms
$>1000$
Hence, $(1.1)^{10000}>1000$