My books says if the following series can not be proved convergent or divergent (even if they can be shown through other tests) through the limit comparison or direct comparison test, then write "NA". If they can be proved, then write CONV or DIV.
The series is as follows:
The books says that that series can't be proved DIV or CONV through the comparison tests.
I have a way, but can't see whats wrong with it. Here is my solution:
let the new series be b_n (because cos(n) will always be negative and in between -1 and 1.... meaning the numerator will always be a lower or equal value than the new series without the cosine. Then with (let this new series be c_n) and this is convergent because as it is a p-series (if you get rid of the 9 which will be irrelevant as ... and so through the direct comparison test, the original series should be convergent because: and c_n is convergent. Where am I going wrong?