Question

Using binomial theorem, indicate which is larger $(1.1{)}^{10000}or1000$.

Answer 1

We have,

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

${=}^{10000}{C}_0{+}^{10000}{C}_1\left(0.1\right){+}^{10000}{C}_2(0.1{)}^2+...{+}^{10000}{C}_{10000}(0.1{)}^{10000}$

$=1+10000\times \left(0.1\right)$+other positive terms

=1+1000 +other positive terms

=1001 +other positive terms > 1000

$\therefore (1.1{)}^{10000}>1000$