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# C1 maths - sequences (proof) Watch

1. There was this question in my text book which I really don't know how to approach at all.

"Prove that the (2n + 1)th term of the sequence Un=n^2 -1, is a multiple of 4."

I started by putting 2n + 1 equal to n^2-1... and then I just went along with it, trying to rearrange it but then realised I was trying to work out n, which isn't what the question asked. So I don't really know how to do this :L

Sorry if the answer's really obvious by the way >.<

And thanks
2. (Original post by monica95)
There was this question in my text book which I really don't know how to approach at all.

"Prove that the (2n + 1)th term of the sequence Un=n^2 -1, is a multiple of 4."

I started by putting 2n + 1 equal to n^2-1... and then I just went along with it, trying to rearrange it
That is right

but then realised I was trying to work out n, which isn't what the question asked.
How?
You do not have an equation

Show what you have done
3. (Original post by monica95)
There was this question in my text book which I really don't know how to approach at all.

"Prove that the (2n + 1)th term of the sequence Un=n^2 -1, is a multiple of 4."

I started by putting 2n + 1 equal to n^2-1... and then I just went along with it, trying to rearrange it but then realised I was trying to work out n, which isn't what the question asked. So I don't really know how to do this :L

Sorry if the answer's really obvious by the way >.<

And thanks
Bold = good
Spoiler:
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Then simply show that a factor of 4 can be taken out of the expression

EDIT: Ninja'd
4. (Original post by TenOfThem)
That is right

How?
You do not have an equation

Show what you have done
Well I actually didn't get to find n as I got stuck lol.
First I thought of (2n+1) equals n. So then I just subbed this in:
(2n+1)= (2n+1)^-1
2n + 1= (2n + 1) (2n + 1) -1
2n= 2n^2 + 4n -2
2n^2 + 4n - 2n=0
Then I tried to factorise that but couldn't.

So then I did:
2n + 1= n^2-1
n^2 -2n -2=0
And then I couldn't factorise that.

Sorry I suck, I know, aha
5. (Original post by monica95)
Well I actually didn't get to find n as I got stuck lol.
First I thought of (2n+1) equals n. So then I just subbed this in:
(2n+1)= (2n+1)^-1
2n + 1= (2n + 1) (2n + 1) -1
2n= 2n^2 + 4n -2
2n^2 + 4n - 2n=0
Then I tried to factorise that but couldn't.

So then I did:
2n + 1= n^2-1
n^2 -2n -2=0
And then I couldn't factorise that.

Sorry I suck, I know, aha
Spoiler:
Show
6. (Original post by monica95)
Well I actually didn't get to find n as I got stuck lol.
First I thought of (2n+1) equals n. So then I just subbed this in:
(2n+1)= (2n+1)^2-1
2n+1 does need to be substituted for n

But the line you have given is nonsense

7. (Original post by TenOfThem)
2n+1 does need to be substituted for n

But the line you have given is nonsense

WOW, I can't believe I expanded that so badly! I don't even realise when I make such stupid mistakes.
So then U2n+1= 4n^2 + 4n
U2n+1= 4(n^2 + n)

Thanks, I get it now
8. (Original post by joostan)
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Thank you

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