Respuesta :
Answer with explanation:
Let the length of string = x unit
⇒When it is cut into half ,
Length of string will be [tex]\frac{x}{2}[/tex]
and when again it is cut into half ,then the length of string will be [tex]\frac{x}{4}[/tex]
and when it is again cut into half length then length of string will be [tex]\frac{x}{8}[/tex].
→And this process continues.
[tex]\text{Length of strings}\rightarrow x , \frac{x}{2}, \frac{x}{4}, \frac{x}{8}, \frac{x}{16},........[/tex]
→If you look at the length of strings , it follows geometric progression having Common ratio equal to [tex]\frac{1}{2}[/tex] 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
[tex]\Rightarrow x \times \frac{1}{2^{n-1}}[/tex]
Let the length of string be [tex]a[/tex] unit
- Length of string when it is cut into half is [tex]\frac{a}{2}[/tex] unit,
- Length of string when again it is cut into half is [tex]\frac{a}{4}[/tex] unit.
- Length of string when it is again cut into half is [tex]\frac{a}{8}[/tex] unit.
And so on
it follows geometric progression having Common ratio equal to [tex]\frac{a}{2}[/tex] .
The length of string will be of negligible length as we cut into more pieces but it will be not equal to Zero.
The length of string after it is cut into n pieces is [tex]\frac{a}{2^{n-1} }[/tex] .
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