Determine if the series converges. A convergent series gets closer and closer to a particular number. To do this, divide one term by the preceding term. Call the result r. If r is greater than -1 and less than +1 the series converges. For example, the series 3, 1.5, .75, .375 .... converges because if we divide one term (say, 1.5) by the preceding one (3) the result (.5) is between -1 and + 1. If the series does not converge, the sum does not exist.
Subtract r from 1. In the example 1 - r = 1 - .5 = .5.
Divide 1 by the result in step 2. In the example, 1/.5 = 2
Multiply this by the first term in the series. This is the sum. In the example, 3*2 = 6. 3 + 1.5 + 0.75 + 0.375 = 6.