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    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
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    (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
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    (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 :ninja:
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    (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
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    (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
    \ 2n+1 \not= (2n+1)^2 -1
    Spoiler:
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    \ U_{2n+1} = (2n+1)^2 -1
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    (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

    U_{2n+1} = (2n+1)^2 - 1 = 4n^2 + 4n + 1 - 1 = ... ....
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    (Original post by TenOfThem)
    2n+1 does need to be substituted for n

    But the line you have given is nonsense

    U_{2n+1} = (2n+1)^2 - 1 = 4n^2 + 4n + 1 - 1 = ... ....
    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
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    (Original post by joostan)
    \ 2n+1 \not= (2n+1)^2 -1
    Spoiler:
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    \ U_{2n+1} = (2n+1)^2 -1
    Thank you
 
 
 
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