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{\Large {Mathematics 2C, Spring 1997}}\\
\large Review for Midterm I
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\begin{enumerate}

\item Limits of Sequences:  Know definition of the limit (no proofs,
but know and be able to explain the ``big picture'');  computation of
limits (a lot of this concerns topics already covered in Math 2A and
Math 2B).  Test your knowledge with questions like p.~646 no.~1, 7, 9,
10, 11, 12, 14, 15.  (The last two need some computations, the rest
you should be able to ``see'' immediately).

\item Recursively defined Sequences: p.~583 no.~41.

\item Series: Finding the limit of a series (if it converges).
Usually impossible, but there are some tricks you should know: The
limit of the geometric series, telescope sums, and partial fractions.

\item Series:  Test for convergence.  Integral Test, Comparison Test,
Quotient Test, Root Test, Alternating Series Test.  Know that
\begin{equation*}
  \sum_{n=0}^\infty a_n
\end{equation*}
diverges if $\displaystyle \lim_{n \to \infty} a_n \neq 0$.  Test your
knowledge with p.~646 no.~ 16, 17, 20, 25, 27, 29.

\item Power Series:  Taylor's Formula.  Given a function $f$, compute
its Taylor Series at some point $a$.  Know tricks to simplify this
task (e.g.\ examples on p.~632 under the red box up to the heading
``Binomial Series'') and p.~635 Examples~7 and~8.

\item Power Series:  Interval of Convergence.  To find the interval of
convergence, use the ratio or the root test for series.  If you want
to test the endpoints, some other methods may be necessary.  Examples:
p.~646 no.~31, 38, 40.  Also, try no.~42 (although this is not a power
series).

\item Series: Remainder.  Know the expression for the remainder in
Taylor's formula, any other expression for the remainder would be
given.  Know what it means and how to use it in a simple context.

\end{enumerate}

General notes:

\begin{itemize}

\item No calculators.  A list of infrequently used formulae will be
supplied, if necessary (integrals, binomial series etc.).

\item If you want to leave from the exam early, you must do so at least 10
minutes before the end of the exam.

\item Remember the \emph{Give Up} option.

\end{itemize}

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