Find the sum of the following infinite geometric series, if it exists: 2/5 + 12/25 +72/125 ...
For a geometric series with first term a and common ratio the sum of infinite terms can be determined if `r < 1` and is equal to `a/(1 - r)`
Here, the first term of the series is 2/5 and the common ratio is 6/5
As `6/5 > 1` it is not possible to find the sum of infinite terms.
For the given series the sum of infinite terms cannot be found.
Common Ratio r = n2/n1 = (12/25)/(2/5) = 6/5 = 1.2
as r is not less than 1 therefore the sum of this series cannot be determined and is infinite.
The sum of infinite terms of a geometric series exists only if r<1 and the sum is equal to a/(1-r) where a is the first term of the series.