MATH1051 Chapter Notes - Chapter 7: Conditional Convergence, Ibm System P, Squeeze Theorem
Document Summary
Recall that an infinite sum is represented as: Notice that a sequence is simply a list of terms but a series is a sum. So you know if your math workbook includes a (cid:494)motivation(cid:495) section, it(cid:495)s a tacit admission that the upcoming material is tedium incarnate. We let denote its nth partial sum, such that: If the sequence partial sum approaches a certain value, then the total sum must as well if you keep extrapolating the partial sum out. That is: is convergent, then the series is said to be convergent. This number is called the sum of the series. Otherwise the series is said to be divergent. Remember, the previous sum which was given by is still a partial sum you(cid:495)re adding (cid:523)-1) from or whatever to. It is often useful to shift the starting point of a series.
