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May 5th, 2018, 03:00 PM   #11
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Quote:
 Originally Posted by Kavesat Thanks for reply, sir. Yes, I have learned some lim like this. Sorry, I can't totally understand what you mean about Σ. If the following Σ is right, why can't you directly replace the k with cos(k) and then calculate? if you can replace, the value will go down - then go up + between -1 and 1...They will neutralize each other. cos1=0.54030230586 cos2=-0.41614683654 cos3=-0.9899924966 cos4=-0.65364362086 cos5=0.28366218546 cos7=0.75390225434
You can of course compute the various cos(k) and add them up to get approximate numeric values. That does not necessarily mean that the sums can be condensed into a simple expression, a so-called closed form.

No, the sums do not neutralize each other, whatever that means. It is true that the various sums oscillate and are sometimes positive and sometimes non-positive, but the oscillation continues forever. It doesn't get to zero and then stay there.
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