Final answer:
Based on the provided information, the name of the Fleischer's first successful series of cartoons cannot be determined. Characters like Betty Boop and Popeye are notable creations by the Fleischer Studios and might be part of their early successes.
Step-by-step explanation:
The Fleischer Brothers created several cartoons in the early stages of animation, with some becoming very successful. However, the name of the Fleischer's first successful series of cartoons is not explicitly mentioned in the provided reference materials. Thus, based on the information you've given, I cannot accurately identify which series was their first success.
It is noted though, that Fleischer Studios created iconic characters like Betty Boop and Popeye the Sailor, which became extremely popular in the 1930s. These characters and their associated series might be among the Fleischer's early successes in the world of cartoon entertainment.