I need some serious help in the attached questions...I need to determine whether the series in the picture converge, absolutely converge ot diverge...

I realy need your guidance and help....

Thanks everyone

My attemp:

I've no clue aboue 1&3...

In 2-I know that cos(n*pi)*ln([n+1]/n ) converges by leibnitz test...But what about the first element in the sum? [sqrt(n)sin(n)tan(1/n^2)] ...