Does the given infinite sum converge?
That's it. Note that in the case of a geometric series, you already know how to answer the question (check the constant ratio) as that was covered in PreCalculus. For the next couple weeks, we'll be studying different arguments for different types of series.
The focus for today is sequences and the main issue is finding the limit of the sequence. In many cases, you already know how to do this b/c it's simply the limit as x-> ∞ that we've already done. The expressions will typically be a little more complicated (involving factorials or combinations of functions for example) and so your thinking will often have to be more nuanced.
The one new tool you'll need is called L'Hospital's Rule. It is used to evaluate limits and applies when direct substitution yields an indeterminate limit of the form 0/0 or ∞/∞.
Notes and examples from today are below.
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