Question

Imagine you have a piece of string. Imagine cutting the string in half, and noting the measure of the piece. If you repeat this process until you cannot cut anymore string in half, what do you suppose happens to the measurement of the strings as the number of pieces rises?

Answer 1

As you get more pieces of string, the string will become smaller. The more you cut it in half the smaller your pieces become

Answer 2

Answer with explanation:

Let the length of string = x unit

⇒When it is cut into half ,

Length of string will be $\frac{x}{2}$

and when again it is cut into half ,then the length of string will be  $\frac{x}{4}$

and when it is again cut into half length then length of string will be  $\frac{x}{8}$.

→And this process continues.

$\text{Length of strings}\rightarrow x , \frac{x}{2}, \frac{x}{4}, \frac{x}{8}, \frac{x}{16},........$

→If you look at the length of strings , it follows geometric progression having Common ratio equal to  $\frac{1}{2}$ that is second string Length divided by first string length.

→The length of string will be of negligible as the number of pieces rises but it will be not equal to Zero.

⇒If you want to find the length of string after it is cut into n parts of , it will be equal to

     $\Rightarrow x \times \frac{1}{2^{n-1}}$