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# Question: Proof by Induction watch

1. Hi everyone, a friend of mine said if I was having any problems with maths that I should come here and I'll be able to get help.

I understand how to do proof by induction. However, I was watching a tutorial video by exam solutions, if you skip to 7:18 and pause, you'll see the steps he took to get it in the form they required. The problem, I'm having is I don't understand how he's doing it. I normally find myself expanding out everything and I usually end up having to factorise quintic equations & cubic equations and etc... Although my way always gives me the correct answer, it takes a very long time. So could someone help me understand what he does please
2. Here's the video http://www.examsolutions.net/maths-r...tutorial-1.php
3. It wont let me link the video one sec guys
4. Guys if you copy and paste this link, I'm sure you'll find the video
Mathematical Induction - Sum of series for r cubed : ExamSolutions
5. (Original post by NinCheng)
Guys if you copy and paste this link, I'm sure you'll find the video
Mathematical Induction - Sum of series for r cubed : ExamSolutions

7:18 on that video, i labelled the lines 1 to 5, which one aren't you understanding?
6. (Original post by DylanJ42)

7:18 on that video, i labelled the lines 1 to 5, which one aren't you understanding?

Line 2. I'm assuming he took the (k + 1)^2 from the one just after k^2.
But the (k+1)^3 is gone and now there is 4(k+1) which I don't understand
7. (Original post by NinCheng)
Line 2. I'm assuming he took the (k + 1)^2 from the one just after k^2.
But the (k+1)^3 is gone and now there is 4(k+1) which I don't understand
If you had something like you would factor out an to get

Now if you had you could factor out an to get alternatively though you could factor out and get

So when he has he is factoring out from both terms.

He does this because the required form needs a at the front, so you may aswell factor it out early and make it easy
8. (Original post by DylanJ42)
If you had something like you would factor out an to get

Now if you had you could factor out an to get alternatively though you could factor out and get

So when he has he is factoring out from both terms.

He does this because the required form needs a at the front, so you may aswell factor it out early and make it easy
Oh, that makes sense.

Thanks!

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