Please list out the name of the test used and the process Th

Please list out the name of the test used and the process. Thank you.

Test the series for convergence or divergence. 1 / n + n cos2 5n

Solution

1/(n+ncos^2(5n))>1/(2n)
<->
by cross multiplying
2n>n+n cos^2(5n)

n>ncos^2(5n)
<->
1>cos^2(5n) which is true

Hence

1/(n+ncos^2(5n))>1/(2n)=1/2*1/n

1/n is known to be divergent

Then 1/(n+ncos^2(5n)) is divergent