--- tags: mth225, dailyprep --- # Daily Prep 5.2 -- MTH 225 ## Overview In this lesson, you'll look at **sums and products** of sequences and get practice using **sigma notation** and **pi notation** for these. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. - Use sigma notation to find a partial sum of a sequence. - Use pi notation to find a partial product of a sequence. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. - Given a sum or product of a sequence, write it using sigma or pi notation. - Determine whether two sums or products are the same, if their sigma or pi notation is different. - Make and prove conjectures about sums that involve binomial coefficients. ## Resources for learning **Video:** Watch this from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 3:42): <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/638638136?h=605e7543c3&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 5.2: Sums and products of sequences"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> **Text:** This material is discussed in the textbook at the very end of [Section 2.1](http://discrete.openmathbooks.org/dmoi3/sec_seq_intro.html). You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. ## Exercises Once you have watched the videos above, go to this form and complete all the non-optional items on it: https://docs.google.com/forms/d/e/1FAIpQLScOUXKguW4-4awzuElisoc44qidy9zp_fQ12U9mVAvgh0QRPw/viewform ## Submission and grading **Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully. **How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you: - Turn the work in before its deadline; - Leave no item blank or skipped, even accidentally; and - Give a good-faith effort at a correct answer on every non-optional item. More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document. When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.