Limit [x->infty] of sum [i=1, x] of cos(i)

[chris84567]

I was wondering what the limit of the sum of cos would be. Would it be 0 because the whole thing would cancel out or something else?

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow \infty}\, \sum_{i=1}^x\, \cos(i)\)

Thanks for any help you can offer.

 

[Deleted member 4993]

I was wondering what the limit of the sum of cos would be. Would it be 0 because the whole thing would cancel out or something else?

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow \infty}\, \sum_{i=1}^x\, \cos(i)\)

Thanks for any help you can offer.

As you have indicated cosine is an oscillating function. Thus the summation does not converge absolutely.

 

[chris84567]

Thus the summation does not converge absolutely.

Is there any rules for sums of oscillating functions.