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