What is the best way to learn sequences/series?

[chans]

I've been doing alright in Calculus II but I can't seem to grasp sequences/series. The different tests like Integral Test, Comparison Test, Ratio/Root Tests also confused me in terms of how to apply them and when to apply them.

What is the best way for me to master this material? Any good sites or tutorials or basic strategies? For integration I learned it well by practicing integrating different integrals with different techniques, but when I try doing it for series/sequences I get stuck and can't retain the concepts.

 

[Simon Bridge]

Same as for anything: do lots of examples - and get a personal tutor.

 

[Entropee]

2 people I always recommend.
Www.patrickjmt.com
http://www.khanacademy.org/math/calculus/sequences_series_approx_calc

It also helps to play around with things like the Cantor set for fun and to familiarize yourself with the techniques used.

 

[Mark44]

I've been doing alright in Calculus II but I can't seem to grasp sequences/series. The different tests like Integral Test, Comparison Test, Ratio/Root Tests also confused me in terms of how to apply them and when to apply them.

This should not confuse you if you pay close attention to the theorems where these rules are presented. Each theorem gives the conditions that must be in place to use the theorem, and what you can conclude when you apply the theorem to your series.

What is the best way for me to master this material? Any good sites or tutorials or basic strategies? For integration I learned it well by practicing integrating different integrals with different techniques, but when I try doing it for series/sequences I get stuck and can't retain the concepts.

 

[yungman]

Do a lot of problems. It is just different from the other calculus stuffs. But as you go higher, there are more and more problems that cannot be solved by traditional integration or differentiations. It often need to be solved by numerical analysis, which is like series and sequence. You are going to encounter much more in Differential Equation and partial differential equation classes. All the Bessels, Legendre etc. are series.

Understand how the function being replaced by series, but after than, it is really a series that sum power of a variable together. That's the reason they called it numerical analysis!