Comparison Test

Jason76

Senior Member
Joined
Oct 19, 2012
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No idea what is going on here. Understand the comparison test. Somehow or another they use the geometric series test as the "other test". Why? :confused: But I do understand the geometric series test.

comparison-test-5.jpg
 
No idea what is going on here. Understand the comparison test. Somehow or another they use the geometric series test as the "other test". Why? :confused: But I do understand the geometric series test.

View attachment 3590
The writer happened to notice that a particular other series would be useful for comparison (hence the "By the comparison test" at the end of the proof), so he used it. And that particular useful other series happened to be a geometric series, so he used that test (hence the "by the geometric series test" under the given restrictions).

At some point, the student needs to become capable of developing things on his own. There may be many valid solution methods; the student needs to learn to find them himself. The posted solution was the one that happened to occur first to the writer. What did you do on your own? ;)
 
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