Question

In two or more complete sentences, explain why the following sequence is an example of a finite series.

Answer 1

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

         $ar^{n-1}=256\\2\times 2^{n-1}=256\\n=8$

Sum of this GP is given by

         $S_n=\frac{a(r^{n}-1)}{r-1}=\frac{2(2^{8}-1)}{2-1}=510$

Since this series have a definite value the series is a finite series.

Answer 2

Answer:

It is finite because it has an ending. Infinite has no ending and will keep going forever while this statement has an ending.

Step-by-step explanation: