Does a geometric series always have a finite value?

Astudy was conducted to determine the proportion of people who dream in black and white instead of color. among 306 people over the age of 55, 68 dream in black and white, and among 298 people under 25, 13 dream in black and white ( based on data from do we dream in color) we want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.