Category Archives: sequences
The Squeeze Theorem And Trigonometric Inequalities
When dealing with sequences and series, we often use inequalities to deal with trig functions. As an example, consider the sequence Does this sequence converge? It’s hard to tell, because behaves strangely for integer values of . Sometimes it’s positive, sometimes it’s negative, and there’s not much of a pattern to it all. However, one … Continue reading
The Squeeze Theorem For Sequences
Last time we saw what a sequence is. Sometimes it can be a bit tricky to figure out what value a sequence converges to, though. One problem is that sequences can switch signs a lot. In this case it’s sometimes useful to use the squeeze theorem, sometimes called the sandwich theorem, to find the limit. … Continue reading
What is a Sequence?
A sequences is just, well, a sequence of numbers. For example, is a sequence, and so is and so is and so is any other sequence of numbers you can think of. No big deal. Often sequences are written with subscript notation, like this Here, is the first term of the sequence, is the third … Continue reading