Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
Question
Which is larger $(1.01)^{1000000}$ or $10,000 ?$
✓
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
$={ }^{1000000} \mathrm{C}_0+{ }^{1000000} \mathrm{C}_1(0.01)+$ 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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