Asymptotic analysis question: sum[log(i)*i^3, {i, n}] is big-theta (log(n)*n^4)
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30-10-2019 - |
سؤال
I've got a homework question that's been puzzling me. It asks that you prove that the function Sum[log(i)*i^3, {i, n}) (ie. the sum of log(i)*i^3 from i=1 to n) is big-theta (log(n)*n^4).
I know that Sum[i^3, {i, n}] is ( (n(n+1))/2 )^2 and that Sum[log(i), {i, n}) is log(n!), but I'm not sure if 1) I can treat these two separately since they're part of the same product inside the sum, and 2) how to start getting this into a form that will help me with the proof.
Any help would be really appreciated. Thanks!
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