Whats the difference between a series and sequence? I was looking at a question earlier that involved sequences and found out that the sequence converged to 0 but the series diverged to infinity. How is that possible? for example the sequence was $a_n$ $=$ $\frac{1}{x_n}$ 
The question was here: Convergence of $x_n=f\left(\frac{1}{n}\right), n\geq 1$ 

A sequence of real numbers is a delineation; more specifically, it is a function from the positive integers into $\mathbb{R}$; e.g., $\lbrace a_{n} \rbrace_{n=1}^{\infty} = a_{1}, a_{2}, \ldots $, where the $a_{i}$ are real numbers.
A series is a summation of a particular sequence.
