The positive integer just greater than ${(1 + .0001)}^{10^{3}}$ is

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
$(1 + 10^{- 4})^{10^{3}}$
$= 1 +^{10^{3}} C_{1} 10^{- 4} +^{10^{3}} C_{2} 10^{- 8} + . . .$
Neglecting higher order terms, we get
$1 + 0.1 + \frac{10^{3} .999}{2} {.10}^{- 8}$
$= 1.1 + \frac{10^{- 5} .999}{2}$
$= 1.1 + \frac{0.0999}{2}$
$= 1.1 + (0.004995)$
$= 1.104995$
$< 2$

Suggest Corrections

Similar questions

(1 + 0.0001)^{1000}

{(1 + 0.0001)}^{10000}

(1 + 0.0001)^{10000}

3

n^{3} + \frac{n (n - 1)}{⌊ 2} (n - 2)^{3} + \frac{n (n - 1) (n - 2) (n - 3)}{⌊ 4} (n - 4)^{3} + . . . . = n^{2} (n + 3) 2^{n - 4}

Question 11

An integer with positive sign(+) is always greater than

(a) 0

(b) 1

(d) 3

Join BYJU'S Learning Program