Calculus: Absolute/Conditional Convergence or Divergence Question

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SUMMARY

The discussion centers on a calculus problem regarding the convergence of a series, specifically addressing the confusion over the summation index. The original question posed by a user involves a series that starts at n=2 and queries whether it can be treated as if it extends to infinity. A consensus was reached that the summation should indeed extend to infinity, as convergence cannot be defined for a finite number of terms. This clarification emphasizes the importance of correctly interpreting series notation in calculus.

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zachem62
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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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