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

Option: 1

4


Option: 2

5


Option: 3

2


Option: 4

3


Answers (1)

best_answer

We know that e=\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^n and 2 < e < 3

\therefore(1+0.0001)^{10000}<3           ( By putting n = 10000 )

\begin{aligned} & Also\ (1+0.0001)^{10000}=1+10000 \times 10^{-4} +\frac{10000 \times 9999}{2 !} \times 10^{-8}+\ldots \ldots\ \ upto\ 10001\ terms \end{aligned}

\Rightarrow(1+0.0001)^{10000}>2 .  Hence 3 is the positive integer just greater than

(1 + 0.0001)10000

    

Hence (d) is the correct option.

 

 

Posted by

sudhir.kumar

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