Infinite Geometric Series Calculator

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Infinite geometric series is an infinite numbered series which has a common ratio ‘r’ between any two consecutive numbers in the series. If the ratio r lies between -1< r <1 then the series converges or else it is a diverging series. The online tool used solve the given infinite geometric series is called as infinite geometric series calculator.

 
Example 1: What is the infinite series 1 + 1/2 + 1/4 + 1/8 + 1/16.....equal to?

 
Given is an infinite series, the first step is to check for the common ratio r.

r = (1/2)/1 = 1/2   r = (1/4)/ (1/2) = 1/2

Hence the common ratio for the geometric series is equal to1/ 2.

The first term a = 1.

Hence sum = a/ (1-r)
 
This gives sum = 1/ (1-1/2) = 1/ (1/2) = 2

1 + 1/2 + 1/4 + 1/8 + 1/16.....  = 2
 


Example 2: What is the infinite series 3 + 1+ 1/3 + 1/9 + 1/27.....equal to?
 
Given is an infinite series, the first step is to check for the common ratio r.

r = (1/3) = 1/3  r = (1/9)/ (1/3) = 1/3

Hence the common ratio for the geometric series is equal to 1/3.

The first term a = 3.

Hence sum = a/ (1-r)
 
This gives sum = 3/ (1-1/3) = 3/ (2/3) = 9/2

3 + 1+ 1/3 + 1/9 + 1/27..... = 9/2






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