Hello, I understand the Limit Comparison Test, but how do you know what you should compare your series to?

Like for http://www.math.unh.edu/%7Ejjp/sol_mixed/img41.gif you should compare it to http://www.math.unh.edu/%7Ejjp/sol_mixed/img42.gif

of which I know diverges so with the L.C.T it will probably diverge. But why is it that you would compare it to 1/n, how do you figure out what you should compare it to? Is it because n/n^2 gives you 1/n or?

Thanks,

Matt