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Summations Explained: Solving Nested Loops & Big‑O Runtime

Published 25, Mar 2026

randerson112358


Description:
In this video, we walk step‑by‑step through how to solve a summation that comes from a nested loop and determine the running time of the code fragment. Using standard summation formulas, we break down the inner and outer loops, simplify the expression, and show why the final result is O(n²).

This is a great walkthrough if you're learning algorithm analysis, preparing for exams, or brushing up on Big‑O notation.

What’s covered:
• Setting up summations for nested loops
• Using summation formulas correctly
• Simplifying inner and outer loops
• Converting the final expression to Big‑O

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►Videos on Big-O Asymptotics:
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Recurrence Relation Run Time by Induction: https://youtu.be/XWykCejG1Rk
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