How to find the sum of the infinite geometric series given 1+2/3+4/9+...?
How to find the sum of the infinite geometric series given ?
Answer & Explanation
Any geometric series' general term can be expressed in the following way:
where is the initial term and the common ratio
In our case we have:
with initial term and common ratio
The general formula for the infinite sum (proved below) is:
So in our case:
The general term of a geometric series can be written:
where is the initial term and is the common ratio.
Given such a series, we find:
Dividing both ends by we get the general finite sum formula:
If then and we find:
So we have the general formula for the infinite sum: