Solving Problems with Harmonic or P-Series - Tips & Tricks

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The discussion centers on the classification of the series 1/n, identifying it as both a harmonic series and a p-series with p=1, which is divergent. Participants agree that while they arrived at the same conclusion regarding divergence, understanding the underlying principles of convergence for p-series is crucial. The conversation emphasizes that correct answers do not always indicate a complete understanding of the concepts involved. Clarity on the conditions for convergence in p-series is highlighted as essential for deeper comprehension. Overall, the dialogue reinforces the importance of grasping the foundational concepts in series analysis.
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Homework Statement


From the example:
blah, blah, blah, = 1/n which is divergent (harmonic serics)

The Attempt at a Solution



blah, blah, blah, =1/n which is a p-series with p=1, therefore divergent.

We both get the same answer, but since all the problems in this section are either convergent or divergent, coming up with the right answer doesn't always mean you did it right.
 
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Uh what is your question actually?
 
You're both right. The sum 1/n is the harmonic series, but is it also a p-series with p=1. Hence, both comments are correct.
 
Although It depends what you know about the conditions on p for convergence.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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