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Interesting Observation of Progression of Perfect Squares

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Joined: 30 Apr 2008
Posts: 1850
Location: Oklahoma City
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Interesting Observation of Progression of Perfect Squares [#permalink]

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29 May 2009, 21:51
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I'm not surew why I just now noticed this, but if you take the progression of perfect squares, you can find the next one by adding the next odd integer to the current perfect square, starting with adding 1 to 0 since 0 is technically the first perfect square.
0 (+1)
1 (+3)
4 (+5)
9 (+7)
16 (+9)
25 (+11)
36 (+13)
49 (+15)
64 (+17)
81 (+19)
100 (+21)
121

You see how the difference in the perfect squares is a pattern?

I have no idea what significance this has, but maybe someone out there with a deeper level of mathematics theory can shed some light on this, as well as explain whether this has any significance.

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SVP
Joined: 07 Nov 2007
Posts: 1757
Location: New York
Re: Interesting Observation of Progression of Perfect Squares [#permalink]

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29 May 2009, 22:27
jallenmorris wrote:

I'm not surew why I just now noticed this, but if you take the progression of perfect squares, you can find the next one by adding the next odd integer to the current perfect square, starting with adding 1 to 0 since 0 is technically the first perfect square.
0 (+1)
1 (+3)
4 (+5)
9 (+7)
16 (+9)
25 (+11)
36 (+13)
49 (+15)
64 (+17)
81 (+19)
100 (+21)
121

You see how the difference in the perfect squares is a pattern?

I have no idea what significance this has, but maybe someone out there with a deeper level of mathematics theory can shed some light on this, as well as explain whether this has any significance.

n , n+1 are consecutive integers

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

So. For any perfect square n^2 to get the next perfect square, we need to add (2n+1).

n=10
n^2 =100
(n+1)^2 = 100 + (2n+1) = 100+(20+1) =121

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Interesting Observation of Progression of Perfect Squares   [#permalink] 29 May 2009, 22:27
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