An infinite sequence is an ordered listing of an infinite number of real numbers, such as ½, ¼, 1/8, 1/16, ... In more formal mathematical language, an infinite sequence is a function whose domain is the set of natural numbers (sometimes with 0 included) and whose range is the set of real numbers. An infinite series is just the sum of all the terms of an infinite sequence. For example, 1/2+1/4+1/8+...+1/2ⁿ+... designates the infinite series whose nth term has the form 1/2ⁿ. In general if the nth term of an infinite series is a_n, then the series is written a₁+a₂+a₃+...+a_n+..., which is also written as ∑a_n where the capital Greek letter ∑ stands for the summation of all terms of the form a_n. Of interest to mathematicians is which infinite series have finite sums and which grow without bound as each new...