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Topic: [ap-calculus] AP Grading for infinite series questions
Replies: 1   Last Post: Mar 30, 2012 6:20 AM

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 Mark Howell Posts: 1,221 Registered: 12/6/04
Re: [ap-calculus] AP Grading for infinite series questions
Posted: Mar 30, 2012 6:20 AM

This question is addressed on page 50 in the Special Focus materials on Series.  There, we say,

"You may be expected to simply
know that a certain series converges or diverges.Typical examples that rarely if ever require justification on the free-response section
of the AP Exam include geometric series, harmonic and alternating harmonic series,
and p-series. Students could simply assert: ?This is the harmonic series. It diverges,?or ?This is the alternating harmonic series. It converges.? "
Now, a question could be formulated in a way that asked students to justify that the harmonic series diverges or that the alternating harmonic converges.  But typically, and particularly in problems asking for an interval of convergence, it's acceptable to appeal to the fact that all of creation knows about these particular cases. ;-)

Mark Howell
Gonzaga College High School
Washington, DC

________________________________
From: Skerbie <skerbie@yahoo.com>

Colleagues,

I know this question has come up numerous times in the 10+ years I've been reading the listserv, but I was unable to find an example in a quick search of the archives.

Here is my question:  Which series can students state as convergent or divergent without further proof?

It's been my understanding that the harmonic and alternating harmonic series are series that students can just state as "divergent" and "convergent," respectively, but are there others?  For example, can they simply state (without further verification) that the latter converges conditionally, i.e., without actually mentioning that sum(1/n) diverges?
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Course related websites:
http://apcentral.collegeboard.com/calculusab
http://apcentral.collegeboard.com/calculusbc
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