The positive integer just greater than (1 + 0.0001)^ 10000 is - Vidyadip

MCQ

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

A
$4$
B
$5$
C
$2$
✓
$3$

✓

Answer

Correct option: D.

$3$

d
(d) We know that $e = \mathop {\lim }\limits_{n \to \infty } \,{\left( {1 + \frac{1}{n}} \right)^n}$ and $2 < e < 3$.

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

Also ${(1 + 0.0001)^{10000}} = 1 + 10000 \times {10^{ - 4}}+ \frac{{10000 \times 9999}}{{2!}} \times {10^{ - 8}} + ......$upto $10001$ terms

$ \Rightarrow {(1 + 0.0001)^{10000}} > 2$.

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

Hence $(d)$ is the correct option.

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