Question

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

2 + 4 + 8 + 16 + ... 256

Answer 1

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

Explanation:

Answer 2

Since there is an ending for the series with 256 this series is an infinite series.

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* 2^(n-1)=256\\n=8`

Sum of this GP is given by

`S_n=(a(r^(n)-1))/(r-1)=(2(2^(8)-1))/(2-1)=510`

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