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Tough Further Maths Question

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)
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×(n−1) 2 \times (n-1) or (n−1)×x2 (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? :h:
(edited 7 years ago)
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RNVS_1299
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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?!
Original post by SeanFM
By (n-1)x2, do you mean 2×(n−1) 2 \times (n-1) or (n−1)×x2 (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? :h:


Here is the question, badboy Sean - Q10
RV.jpg
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 :h:
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 Sn+1=1(n+1)+2(n)+3(n−1)+...+(n)2+(n+1)1 \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 Sn \displaystyle S_n so you can write Sn+1 \displaystyle S_{n+1} on one line and Sn \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
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 :h:


Jheeze Sean, uni stress hitting u again!!!

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