plotting summation to check for convergence

Our assignment was to enter in a series and check to see if it converges by graphing.

However, when I attempt to graph it, I get a bunch of errors that I'm not sure what they mean. Best way to show it is a picture

I'm not 100% sure that the "Sum does not converge" is accurate, because I dont think it would be assigned if it didn't. so maybe I entered in the series wrong? can anyone offer some enlightenment here?

• is n the number of terms in the sum? it should appear on the right hand side of s[n_] – user64620 Dec 16 '15 at 21:12
• Please include correctly formatted, copy-and-pastable code in your post, not screenshots; possible answerers don't like to use their valuable (literally-)free time re-writing code into Mathematica and running it. You can edit your post by clicking the grey button at the bottom of your post, and you can click the grey question mark at the right of the toolbar for formatting help. That said, you probably want to replace the Infinity with n on the right-hand side of the s[n_] definition. The infinite sum doesn't converge, so you have to do a finite sum, as it seems you are attempting. – march Dec 16 '15 at 21:19
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• The series does not converge. The terms (1/cube root(k)) are larger than the harmonic series (Sum of 1/k) which does not converge. No need for a computer program. – user48709 May 8 '17 at 18:46
• @user48709 I moved your answer to comment, you couldn't due to reputation restrictions. The question was to "check to see if it converges by graphing", so while your comment is on topic, it does not provide the answer the this specific question. – Kuba May 8 '17 at 19:37

ListPlot[Accumulate[Table[1/CubeRoot[n], {n, 1, 5000}]]]

Limit[Sum[1/CubeRoot[k], {k, 1, n}], n -> Infinity]

ListLinePlot@Table[Sum[1./CubeRoot[k], {k, 1, n}], {n, 100}]