\[S_n\]
for the sum of the first \[n\]
terms of a series. The \[n\]
th term is given by \[a_n=S)n-S_{n-1}\]
.Example:
\[S_n==n^3+2n-2\]
.\[S_{n-1}=(n-1)^3+2(n-1)-2=n^3-3n^2+3n-1+2m-2-2=n^3-3n^2+5n-5\]
\[\begin{equation} \begin{aligned} a_n &=S_n-S_{n-1} \\ &= (n^3+2n-2)-(n^3-3n^2+5n-5) \\ &= 3n^2-3n+3(n^3+2n-2) \end{aligned} \end{equation}\]