Using Binomial Theorem, indicate which number is larger (1.1) ^ 1… - Vidyadip

Question

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

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Answer

$(1.1)^{10000}=(1+0.1)^{10000}$
$=1+{ }^{10000} \mathrm{C}_1(0.1)+{ }^{10000} \mathrm{C}_2(0.1)^2+{ }^{10000} \mathrm{C}_3(0.1)^3+\ldots .$
$=1+10000(0.1)+\text { other positive numbers }$
$=1+1000+\text { other positive numbers }$
Which is greater than 1000 .
Thus (1.1)10000 > 1000

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