Using Binomial Theorem, indicate which number is larger (1.1)^ 10… - Vidyadip

Question

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

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Answer

$(1.1)^{10000} = (1 + 0.1)^{10000}.$
$= 1 +\ ^{10000}C_1(0.1) +\ ^{10000}C_2(0.1)^2 +\ ^{10000}C_3(0.1)^3 + ....$
$= 1 + 10000 (0.1) +$ other positive numbers
$= 1 + 1000 +$ other positive numbers
Which is greater than $1000.$
Thus $(1.1)10000 > 1000$

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