Which is larger (1.01)^ 1000000 or 10,000? - Vidyadip

Question

Which is larger $(1.01)^{1000000}$ or $10,000?$

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Answer

Splitting $1.01$ and using binomial theorem to write the first few terms we have
$(1.1)^{10000} = (1 + 0.1)^{10000}$. Using binomial theorem
$=\ ^{1000000}C_0 +\ ^{1000000}C_1(0.01) +$ other positive terms
$= 1 + 10000 (0.01) +$ other positive terms
$= 1 + 1000 +$ other positive terms
$> 10000.$
Therefore,$(1.01)^{1000000} > 10000$

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