The positive integer just greater than $${\left( {1 + 0.0001} \right)^{10000}}$$    is

Solution :
$$\eqalign{ & {\left( {1 + 0.0001} \right)^{10000}} = {\left( {1 + \frac{1}{n}} \right)^n},n = 10000 \cr & = 1 + n.\frac{1}{n} + \frac{{n\left( {n - 1} \right)}}{{2!}}\frac{1}{{{n^2}}} + \frac{{n\left( {n - 1} \right)\left( {n - 2} \right)}}{{3!}}\frac{1}{{{n^3}}} + ..... \cr & = 1 + 1 + \frac{1}{{2!}}\left( {1 - \frac{1}{n}} \right) + \frac{1}{{3!}}\left( {1 - \frac{1}{n}} \right) + \left( {1 - \frac{2}{n}} \right) + ..... < 1 + \frac{1}{{1!}} + \frac{1}{{2!}} + \frac{1}{{3!}} + ..... + \frac{1}{{\left( {9999} \right)!}} \cr & = 1 + \frac{1}{{1!}} + \frac{1}{{2!}} + .....\,\infty = e < 3 \cr} $$