Summation Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

Summation (Sigma) notation is a prerequisite for talking concisely about the sums of areas that underlie definite integrals. “Sigma (Summation) Notation” in section 5.1 of our textbook introduces some basic ideas and laws for summations, and this discussion gives you a chance to talk about and practice using that notation.

Ask questions about, comment on, or answer one or more of the following questions:

By carrying out the additions by hand, can you evaluate...

1. \[\sum_{i=1}^3 2i-1\]
2. \[\sum_{k=2}^4 \frac{1}{k}\]

Can you use summation notation to express the sum 3+4+5+6+...+99+100? How about the sum 0+1+3+7+15+...+63+127+255? Are some sums easier to express using summation notation than others? If so, what makes a sum “easy” rather than “hard” to express this way?

By using algebra and summation laws, can you evaluate...

1. \[\sum_{i=1}^{100} i\]
2. \[\sum_{j=1}^{10} 3j^2+\frac{j}{2}\]
3. \[\sum_{i=10}^{100} i\]
4. \[\sum_{i=1}^{n-1} 3i-2\]