A) 4
B) 5
C) 2
D) 3
Correct Answer: D
Solution :
| [d] \[{{(1+0.0001)}^{10000}}={{\left( 1+\frac{1}{n} \right)}^{n}},n=10000\] |
| \[=1+n.\frac{1}{n}+\frac{n(n-1)}{2!}\frac{1}{{{n}^{2}}}+\frac{n(n-1)(n-2)}{3!}\frac{1}{{{n}^{3}}}+....\] |
| \[=1+1+\frac{1}{2!}\left( 1-\frac{1}{n} \right)+\frac{1}{3!}\left( 1-\frac{1}{n} \right)\left( 1-\frac{2}{n} \right)+....\] |
| \[<1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+.......+\frac{1}{(9999)!}\] |
| \[=1+\frac{1}{1!}+\frac{1}{2!}+......\infty =e<3\] |
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