Question

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

Answer 1

By splitting \(1.1\) and then applying Binomial Theorem, the first few terms of \((1.1)^{10000}\) can be obtained as

\((1.1) ^{10000} = (1+0.1)^{ 10000}\)
=\(^{10000}C_0 + ^{10000}C_1(1.1)\,+\,\text{Other positive terms}\)
=\(1+10000×1.1+ \text{Other positive terms }\)
=\(1+11000+\text{Other positive terms}\)
\(> 1000\)

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