The sum of the infinite series 1 − 1/3 + 1/9 − 1/27 + … is:

This is a geometric series with a = 1 and r = −1/3. Since |r| < 1 the sum to infinity is a/(1 − r) = 1/(1 + 1/3) = 1/(4/3) = 3/4. (Ignoring the minus sign and using r = 1/3 gives the wrong value 3/2.)