Determent the convergence of the series ( 4 + Abs(Cos(k)) ) / k^3

[DavidM97]

So I've been trying to figure out weather or not the series from k=1 to Infinity of the function (4+Abs(Cos(k)))/k^3 converges.

I've tried comparing it to just the function 4/k^3 which is a smaller series, but that doesn't work because it is a p-series where p=3>1 which converges.

Can anyone please help me?

Thank you in advance.

 

[stapel]

So I've been trying to figure out weather or not the series from k=1 to Infinity of the function (4+Abs(Cos(k)))/k^3 converges.

I've tried comparing it to just the function 4/k^3 which is a smaller series, but that doesn't work because it is a p-series where p=3>1 which converges.

Can anyone please help me?

Try using what you know about the range of values for cosine.