Using binomial theorem, indicate which is larger (1.1)^ 10000 or … - Vidyadip

Question

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

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Answer

We have,
$(1.1)^{10000}=(1+0.1)^{10000}$
$={^{10000}\text{C}}_0+{^{10000}\text{C}}_1(0.1)+{^{10000}\text{C}}_2(0.1)^2+...+{^{10000}\text{C}}_{10000}(0.1)^{10000}$
$= 1 + 10000 \times (0.1) +$ other positive terms
$= 1 + 1000 +$ other positive terms
$= 1001 +$ other positive terms $> 1000$
$\therefore (1.1)^{10000}> 1000$

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