How to tell the difference in series

[Kendall Pecere]

Hey all! I am in Calculus 2, and we are starting to get into series. This may seem like an odd question, but on quizzes I seem to have difficulty identifying the type of series in order to be able to properly work it, and I'd like to have this down before I get to the test. Does anybody have a good way of identify whether a series is arithmetic? Geometric? P-series? Harmonic? Professor hasn't really given any suggestions other than to just kind of eyeball it, and that only works to a certain degree. Thanks in advance for any replies!

 

[Mark44]

Moved from HW section as this is not specifically a homework question. @Kendall Pecere, if you post a question in the homework section, you must use the homework template.

 

[Ray Vickson]

Hey all! I am in Calculus 2, and we are starting to get into series. This may seem like an odd question, but on quizzes I seem to have difficulty identifying the type of series in order to be able to properly work it, and I'd like to have this down before I get to the test. Does anybody have a good way of identify whether a series is arithmetic? Geometric? P-series? Harmonic? Professor hasn't really given any suggestions other than to just kind of eyeball it, and that only works to a certain degree. Thanks in advance for any replies!

What is the definition of an arithmetic series? Does your given series (if you have one) satisfy that definition? Same questions for "geometric" or "p-series". I am not sure what definition your instructor uses for "harmonic series", but as far as I know there really is only one such series, up to a multiplicative constant, maybe.

 

[geoffrey159]

If you are starting on series, I think it is more likely you get questions regarding convergence-divergence rather than computing the sum of converging series which often require knowledge on power series and Fourier series. Maybe you can be asked to evaluate the sum of geometric and telescopic series, as well as Cauchy products, and double series in easy cases.

I'd say that for a first test, you need to be solid on convergence.