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NP Chapter 2 Page 62 Exercise 17

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ray_serrano
 Post subject: NP Chapter 2 Page 62 Exercise 17
 Post Posted: Thu Apr 23, 2009 6:59 am 
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Course Students


Posts: 10
I can see how we get to k2 = 4n^2 -4n + 1, using FOIL. But how do we factor to k = 4n(n-1)+1?
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twallack
 Post subject: Re: NP Chapter 2 Page 62 Exercise 17
 Post Posted: Sat May 02, 2009 9:45 am 
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Students


Posts: 2
I thing that's an error in the book. The left side of the equation shouldn't change.
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RonPurewal
 Post subject: Re: NP Chapter 2 Page 62 Exercise 17
 Post Posted: Sun May 03, 2009 5:13 am 
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ManhattanGMAT Staff


Posts: 7146
ah yes, that should be k^2, not k.

we just pulled the 4n out of the first two terms. that's a bit of an ingenious transformation - it's probably not something i would think to do, for instance, and i teach the test!

i'll call attention to the error.

--

by the way, if you ever see something like this on the real test, you're probably better off not looking for this sort of mathe-magic.

instead, just do PATTERN RECOGNITION. plug in a bunch of numbers and look for a pattern.

if k = 2n - 1, then the first k's that come to mind are 1, 3, 5, 7, and 9.
k = 1 --> k^2 = 1, remainder 1
k = 3 --> k^2 = 9, remainder 1
k = 5 --> k^2 = 25, remainder 1
k = 7 --> k^2 = 49, remainder 1
k = 9 --> k^2 = 81, remainder 1

the pattern is clear.
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