help i need to simplify this equation.step by step.please asap?

Question

2+(n-1)2+1/2(n-1)(n-2)1

the 1/2 counts as a half. i really need help with simplifying this equation asap for a piece of coursework, its the only one that doing my head in now. i need a step by step break down of it. thank you for your help

Answer 1

2+(n-1)2+1/2(n-1)(n-2)1
= 2 + 2n - 2 + (1/2)(n^2 - 2n - n + 2)
= 2n + (1/2)(n^2 - 3n + 2)
= 2n + (1/2)n^2 - (1/2)(3n) + (1/2)2
= 2n + (1/2)n^2 - (3/2)n + 1
= (1/2)n^2 + (1/2)n + 1

Answer 2

There are two different ways of defining a perfect shuffle. Both ways involve splitting the 52 card deck exactly in half and then "interweaving" the two halves so that cards in odd positions are from one half and the cards in even positions are from the other half. The two ways of perfectly shuffling have, respectively, ABABABAB... and BABABABA... configurations, where A = from the top 26 of the deck and B = from the bottom 26.

The perfect shuffle that Marilyn is presumably talking about (whether she in fact knows this or not) is the ABABABAB... shuffle. Enumerate the cards 1 to 52 from the top to the bottom of the deck. We get the following equations:

if 1<=x<=26, then x -> 2x-1 (card in position x goes to position 2x-1)
if 27<=x<=52, then x -> 2(x-26) = 2x-52
Notice that 2x-1 = 2x-52 modulo 51. Therefore, we can merge these two equations into this Fundamental Equation:
x -> 2x-1 mod 51

At first, you may say, "Wait! 1=52 mod 51, and that creates a problem." In fact, it doesn't because it's obvious that the 1 card stays in the 1 position throughout, so there's no chance of a mix up.

Now, we want to know what the Fundamental equation gives after 8 iterations.

1 iteration: 2x-1
2 iterations: 2(2x-1)-1 = 4x-3
3 iterations: 2(2(2x-1)-1)-1 = 8x-7
n iterations: (2^n)x - (2^n -1)
8 iterations: 256x - 255

Answer 3

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Answer 4

I got the same answer as other people

2+(n-1)2 + 1/2(n-1)(n-2)
=(2 + (2n-2)) + 1/2((n^2)+(-n-2n)+(-2)(-1))
=(2 + (2n-2)) + 1/2(((n^2)-3n)+2)
=2n + (n^2-3n + 2)/2
=4n/2 + (n^2-3n + 2)/2
=(n^2 + n + 2) / 2

Answer 5

2+(n-1)2+1/2(n-1)(n-2)
if it is like this
2+2n-2+1/2(n^2-3n+2)
2n+1/2(n^2-3n+2)
take lcm
(4n+n^2-3n+2)/4
(n^2+n+2)/4

Answer 6

This is not an equation since this information is not stated to be equal to anything else i.e. there is no "=" sign.

Answer 7

2+(n-1)2+1/2(n-1)(n-2)1
2+2n-2+(1/2)(n^2-3n+2)
2+2n-2+n^2/2-3n/2+1
n^2/2+n/2+1

Answer 8

i was gona ansswer it but wat the **** this guy above is right