A geometric series with first term 3 converges to the sum of 2. Find the common ratio of the series

Answer 1

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.