# Asymptotic Analysis of Sum

I want to do an analysis on the sum $\Sigma_{i=0}^n f(i)$. All that is known about $f(i)$ is that $f(i) \in \Theta (i \log i )$.

How do I do this?

• Welcome to Computer Science! What have you tried? Where did you get stuck? We do not want to just hand you the solution; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for tips on asking questions about exercise problems. If you are uncertain how to improve your question, why not ask around in Computer Science Chat? – Raphael Feb 7 '17 at 18:00
• Hint: Unfold the definition of "$f \in \Theta(\dots)$". You will have to do two proofs/calculations for bounds on the sum. Be careful about making $n_0$ large enough. – Raphael Feb 7 '17 at 18:01
• @Raphael I believe there's a quicker solution based on Stirling here. – quicksort Feb 7 '17 at 18:05
• Approximate the sum by an integral. – Yuval Filmus Feb 7 '17 at 21:03