In this video we prove by induction that the sum of i^2 from 0 to n is equal to (n(n+1)(n+2))/6 for all natural numbers n. We right out all the steps explicitly so that is it a suitable answer such that to get full marks on an exam.
In this question:
1. We need to know how to use algebraic manipulation to get our desired expression.
2. We know the rules of summation such as the case where the first and last number of the summation are the same.
3. We need to know how to split a summation.
4. We need to know the basic structure of a proof by induction answer.
You can get some practice by attempting the problem on your own before watching the rest of the video.
Feel free to comment a question you would like me to solve below.
Chapters:
0:00 Introduction
0:18 Base Case
2:06 Induction Hypothesis
3:11 Inductive Step
12:18 Conclusion