Executive functions (also known as cognitive control and supervisory attentional system) is an umbrella term for the management (regulation, control) of cognitive processes, including working memory, reasoning, task flexibility, and problem solving as well as planning and execution.
Definition of finite. 1  1a : having definite or definable limits a finite number of possibilitiesb : having a limited nature or existence finite beings. 2  2 : completely determinable in theory or in fact by counting, measurement, or thought the finite velocity of light.
The sum of a geometric series is finite as long as the absolute value of the ratio is less than 1; as the numbers near zero, they become insignificantly small, allowing a sum to be calculated despite the series containing infinitely-many terms. The sum can be computed using the self-similarity of the series.