Problem-Solving: Fall-2024
W1 D2 Practice: Due W1 D2

1. Series Notation 1

   Write out the first four nonzero terms in the series:

   1. \[\sum\limits_{n=0}^\infty \frac{1}{n!}\]

   2. \[\sum\limits_{n=1}^\infty \frac{(-1)^n}{n!}\]
   3. \begin{equation} \sum\limits_{n=0}^\infty {(-2)^{n}\,\theta^{2n}} \end{equation}

2. Series Notation 2

   Write (a good guess for) the following series using sigma \(\left(\sum\right)\) notation. (If you only know a few terms of a series, you don't know for sure how the series continues.)

   1. \[1 - 2\,\theta^2 + 4\,\theta^4 - 8\,\theta^6 +\,\dots\]

   2. \[\frac14 - \frac19 + \frac{1}{16} - \frac{1}{25}+\,\dots\]