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