Tough Further Maths Question

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    If Sn=n + 2(n-1) + 3(n-2)+...+(n-1)x2 +nx1, where n is a positive integer,
    prove that Sn+1 - Sn=1/2(n+1)(n+2)
    prove that Sn= 1/6(n)(n+1)(n+2)
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    (Original post by RNVS_1299)
    If Sn=n + 2(n-1) + 3(n-2)+...+(n-1)x2 +nx1, where n is a positive integer,
    prove that Sn+1 - Sn=1/2(n+1)(n+2)
    prove that Sn= 1/6(n)(n+1)(n+2)
    By (n-1)x2, do you mean  2 \times (n-1) or  (n-1) \times x_2 ? If it's the latter the sequence looks rather strange to me.

    Also, what have you tried / what are your thoughts?
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    Hi,

    For what you asked, it is 2(n-1).

    Ive tried quite a few things,but I end up with a sequence that has r and n in it as variables which obviously wont work, so I Dont know how to go about doing this?!
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    (Original post by SeanFM)
    By (n-1)x2, do you mean  2 \times (n-1) or  (n-1) \times x_2 ? If it's the latter the sequence looks rather strange to me.

    Also, what have you tried / what are your thoughts?
    Here is the question, badboy Sean - Q10
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    (Original post by RNVS_1299)
    Hi,

    For what you asked, it is 2(n-1).

    Ive tried quite a few things,but I end up with a sequence that has r and n in it as variables which obviously wont work, so I Dont know how to go about doing this?!
    (Original post by Chittesh14)
    Here is the question, badboy Sean - Q10
    Have spent some time on it but can't get my head around it. Sorry! Maybe someone else can have a go
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    (Original post by RNVS_1299)
    If Sn=n + 2(n-1) + 3(n-2)+...+(n-1)x2 +nx1, where n is a positive integer,
    prove that Sn+1 - Sn=1/2(n+1)(n+2)
    prove that Sn= 1/6(n)(n+1)(n+2)
    so  \displaystyle S_{n+1} = 1(n+1) + 2(n) + 3(n-1)+...+(n)2 +(n+1)1 .

    there are n+1 terms here and n terms in  \displaystyle S_n so you can write  \displaystyle S_{n+1} on one line and  \displaystyle S_n on the line below like so;

    http://imgur.com/a/QufU5

    from there its fairly straightforward.

    The next part is just proof by induction
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    (Original post by SeanFM)
    Have spent some time on it but can't get my head around it. Sorry! Maybe someone else can have a go
    Jheeze Sean, uni stress hitting u again!!!
 
 
 
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