Answer:
Since there is an ending for the series with 256 this series is an infinite series.
Step-by-step explanation:
The definition of a finite series is given as the sum of finite number of terms. That means it is having a finite value since we are adding a finite number of terms. An infinite series is the summation of infinite number of terms, so it does not have finite value.
Here the given example is 2 + 4 + 8 + 16 + ... 256
Since there is an ending for the series with 256 this series is a finite series.
This is an example of Geometric progression
We have
[tex]ar^{n-1}=256\\2\times 2^{n-1}=256\\n=8[/tex]
Sum of this GP is given by
[tex]S_n=\frac{a(r^{n}-1)}{r-1}=\frac{2(2^{8}-1)}{2-1}=510[/tex]
Since this series have a definite value the series is a finite series.
