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

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Solution

The correct option is D 3
$(1 + 0.0001)^{10000}$

$= (1 + \frac{1}{10000})^{10000}$

$= (1 + \frac{1}{n})^{n} = n_{C_{0}} (1)^{n} + n_{C_{1}} (1)^{n - 1} . \frac{1}{n} + n_{C_{2}} (1)^{n - 2} \frac{1}{n^{2}} + . . .$

$= 1 + n . \frac{1}{n} + \frac{n (n - 1)}{2} . \frac{1}{n^{2}} + . . .$

$= 2 + \frac{n (n - 1)}{2 n^{2}} + . . . > 2$
Integer just greater than 2 is 3.

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