Question:
The positive integer just greater than $(1 + 0.0001)^{10000}$ is
The positive integer just greater than $(1 + 0.0001)^{10000}$ is
Updated On: Jul 5, 2022
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The Correct Option is D
Solution and Explanation
$\left(1+ 0.0001\right)^{10000} = \left(1+ \frac{1}{n}\right)^{n} , n =10000$
$ = 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}} + ..... $
$= 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)!} $
$ = 1 + \frac{1}{1!} + \frac{1}{2!} + ..... \infty= e < 3 $
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Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
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