This is certainly curious, since the first term in your series isn't even defined!
Problem: In each of the following, use the integral test (if possible) to determine whether the given series converges. (NOTE: Before applying the I.T., you must be sure your function f(x) is continuous, decreasing, and non-negative on the interval [1, )
I'm not sure exactly how to approach this problem, but I started out with the supposition that the I.T. can't be applied since the function isn't continuous on the interval [1, ). Is this correct? If so, I was thinking of using the Limit Comparison Test next, but I wasn't sure what similiar function to pick...I tried but that limit wasnt finite, so now I'm stuck. Can someone help me get on the right track? Thanks is advance.
is what might referred to as a known result. "Known results" are sort of your toolbox from which you draw comparisons. You know that (...) 1/n diverges by p-series test, so you can use it to show convergence (divergence) of "smaller" ("bigger") sums.
If you "know" the result that Plato cites, then you can use it to show what he showed.