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# FP1 Proof By Induction, stuck on induction step watch

1. Hello
I'm currently doing one question of chapter 6 of FP1, but I am stuck of how to simply this down.
The question is:
Prove by Mathematical Induction that:

Now I have been able to do the basic step and the assumption step. I started the induction step when n=k+1 and I got to the stage where I had to simplify the equation:

Now is there a way of simplifying this expression, for I tried to use the internet and the textbook, but it doesn't seem to explain it. Sorry if this seems to be a silly question. Thanks
2. (Original post by cpdavis)
Hello
I'm currently doing one question of chapter 6 of FP1, but I am stuck of how to simply this down.
The question is:
Prove by Mathematical Induction that:

Now I have been able to do the basic step and the assumption step. I started the induction step when n=k+1 and I got to the stage where I had to simplify the equation:

Now is there a way of simplifying this expression, for I tried to use the internet and the textbook, but it doesn't seem to explain it. Sorry if this seems to be a silly question. Thanks
Take out a factor of
3. (Original post by cpdavis)
Hello
I'm currently doing one question of chapter 6 of FP1, but I am stuck of how to simply this down.
The question is:
Prove by Mathematical Induction that:

Now I have been able to do the basic step and the assumption step. I started the induction step when n=k+1 and I got to the stage where I had to simplify the equation:

Now is there a way of simplifying this expression, for I tried to use the internet and the textbook, but it doesn't seem to explain it. Sorry if this seems to be a silly question. Thanks
take a factor of 0.25(k+1)^2 out,
youll get 0.25(k+1)^2 (k^2 +4(k+1))
and it turns out to factorise to 0,25(k+1)^2 (k+2)^2 which is the form you want,

hope it helps (:
4. As everyone else has said....

However, look at the form of the result you are trying to achieve. You can see that n^2 is a factor, hence you would be looking for (k+1)^2 as a factor in the induction step.
5. Thanks Everyone! Repping everything before this post!

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