Chapter 6 Sequences & Series
“All the instruments have been tried save one, the only one precisely that can succeed: well-regulated freedom.” - Jean-Jacques Rousseau
Intuitively speaking, a sequence may be thought of as a list of numbers and a series may be thought of as the sum of a sequence of numbers. The sequence below is approaching \(0.\) Does the series below add up to a number, or as we keep adding terms, do the sums tend to infinity?
\begin{equation*}
\mbox{Sequence: } 1, 1/2, 1/3, 1/4, \dots
\end{equation*}
\begin{equation*}
\mbox{Series: } 1 + 1/2 + 1/4 + 1/8 + \dots
\end{equation*}