Question

Find a positive number small than
$\frac{1}{2} {}^{100} .$
Justify. ​

Answer 1

Answer:

We know 1/2 = 0.5.

1/22 = (0.5)2 = 0.25.

1/23 = (0.5)3 = 0.125.

1/24 = (0.5)4 = 0.0625.

⋮

1/21000 = (0.5)1000 ≅ 0.

There will not be a positive number smaller than 0.

So there will not be a +ve number smaller than 1/21000

$\huge\mathfrak\red{Dishant}$

Answer 2

$\frac{1}{2} {2}^{} < \frac{1}{2} {2}^{} < \frac{1}{2} {3}^{} < ....$

$\frac{1}{2} = 0.5 \: \frac{1}{2} {2}^{} = \frac{1}{4} = 0.25 \: \\ \\ \frac{1}{2} { {3}^{} } = \frac{1}{8} = 0.125$

$\frac{1}{2} {100}^{} < \frac{1}{2} {101}^{}$

$The \: smaller \: positive \: number \: than \: 2 {}^{100} \\ \: is \: 2 {}^{101} .$

Explanation:

$@PopularANSWERER$