Write down any two sequential terms of the geometric series, preferably the first two. For example, if your series is 3/2 + -3/4 + 3/8 + -3/16 + .. your can use 3/2 and -3/4.
Divide the second term by the first term to find the common ratio. To divide fractions, flip the divisor and make it multiplication. Using the previous example with 3/2 and -3/4, the common ratio is (-3/4)/(3/2) = (-3/4)*(2/3) = -6/12 = -1/2.
Use the common ratio, the first term and the total number of terms to calculate the sum of the series. If you have a finite number of terms, use the formula "a*(1-r^n)/(1-r)", where "a" is the first term, "r" is the common ratio and "n" is the number of terms. Use the formula "a/(1-r)" if the series is infinite, where "a" is the first term and "r" is the common ratio. The terms must approach 0 for the series to converge and have a sum. Using the previous example, the common ratio is -1/2, the first term is 3/2 and the series is infinite, so the sum is "(3/2)/(1-(-1/2)) = 1."