A geometric series with first term 3 converges to the sum of 2. Find the common ratio of the series
We know that the sum of a geometric series with first term a and common ratio r is given by:
S = a / (1 - r)
In this case, the first term is 3 and the sum is 2. So we have:
2 = 3 / (1 - r)
Multiplying both sides by (1 - r), we get:
2 - 2r = 3
Simplifying, we get:
-2r = 1
Dividing both sides by -2, we get:
r = -1/2
Therefore, the common ratio of the series is -1/2.