Using binomial theorem, indicate which is larger $(1.1)^{10000}$ or $1000$ .

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Solution

$(1.1)^{10000} = (1 + 0.1)^{10000}$

$= 10000_{C_{0}} + 10000_{C_{1}} (1.1)$ + other positive terms

$= 1 + 10000 \times 1.1$ + other positive terms

$= 1 + 11000$ + other positive terms

$> 1000$

Hence, $(1.1)^{10000} > 1000$ .

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