Calculus: Absolute/Conditional Convergence or Divergence Question

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The discussion revolves around a calculus problem concerning the convergence of a series that incorrectly specifies the summation limit as n instead of infinity. Participants clarify that the series should indeed sum from n=2 to infinity, as convergence cannot be determined for a finite number of terms. The consensus is that treating the series as if it extends to infinity is the correct approach. This highlights the importance of accurate notation in mathematical problems. The resolution emphasizes that the original problem likely contains a typographical error.
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Homework Statement



This is the problem:

http://i.imgur.com/AtISqng.jpg

its the first series, not the second one with the cos

Homework Equations


The Attempt at a Solution



so anyways i did this question but i just had one doubt. in every other question like this that I've done, the series summation goes from n=1 or something and goes to infinity. in this question, the summation starts at n=2 and goes to...just n. so can i solve this just as if the summation was going to infinity or do i have to do it differently?

Thanks!
 
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That is undoubtedly a typo and should go to infinity. There would be no notion of convergence for a finite number of terms plus it makes no sense for an index to go to itself.
 
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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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