Trick of the Day - Sum of squares in a Fibonacci Sequence

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Trick of the Day - Sum of squares in a Fibonacci Sequence

Post by Ani on Wed Feb 25, 2009 8:12 pm

Well, the name is a bit misleading.
Since I'm LaTEX nub, I'll have to use "^" as a power symbol
oh, and in addition, since I'm not in the computer lab for french, expect the tricks at this time of day now.

What I mean by Sum of Squares in a Fibonacci Sequence is as follows:

1^2 + 1^2 + 2^2 + 3^2 + 5^2
in essence, "one squared plus one squared plus two squared" and so on

So, heres the trick

ex. 1 - 1^2 + 1^2 + 2^2 + 3^2 + 5^2
1. find the next term (8^2 in our case since 3 + 5 = Cool and remember it
2. Now, the most important part: IGNORE ALL THE SQUARES and multpily the 8, NOT THE 8^2 to the last term and remember the number ( (40 in our case since 8*5 = 40 Remember, it is 8*5 b/c you FORGET ABOUT THE SQUARES)
3. now, find the term which comes before the first term (0^2 in our case since 1-1 = 0)
4. You guessed it, FORGET ABOUT THE SQUARES and multiply the before term with the first term (0 in our case since 0*1 = 0)
5. Subtract the second number (0) from the first number (40), and you get your answer (40).

Now, practice young padawan

1. 1^2 + 2^2 + 3^2 + 5^2 + 8^2
2. 1^2 + 2^2 + 3^2 + 5^2 + 8^2 +13^2
3. 1^2 + 5^2 + 6^2 + 11^2 + 17^2
4. 1^2 + 10^2 + 11^2 + 21^2
5. 1^2 + 3^2 + 4^2 + 7^2 + 11^2
6. 2^2 + 3^2 + 5^2 + 8^2 + 13^2
7. 9^2 + 10^2 + 19^2
8. 1^2 + 2^2 + 3^2 + 5^2 + 8^2 + 13^2 + 21^2
9. 1^2 + 2^2 + 3^2 + 5^2 + 8^2 + 13^2 + 21^2 + 34^2
10. 5^2 + 6^2 + 11^2 + 17^2


Last edited by Ani on Wed Mar 04, 2009 6:08 pm; edited 2 times in total
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Re: Trick of the Day - Sum of squares in a Fibonacci Sequence

Post by HTang on Tue Mar 03, 2009 11:54 am

That last step should be "Subtract the second number from the first number," else you get -40 for your answer.
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Re: Trick of the Day - Sum of squares in a Fibonacci Sequence

Post by Ani on Tue Mar 03, 2009 7:04 pm

HTang wrote:That last step should be "Subtract the second number from the first number," else you get -40 for your answer.
Heeded
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Re: Trick of the Day - Sum of squares in a Fibonacci Sequence

Post by HTang on Tue Mar 03, 2009 11:52 pm

You swapped the quoted numbers too, which makes the point still valid, as you still end up with -40 as an answer. 40 is the first number, and 0 is the second number.
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Re: Trick of the Day - Sum of squares in a Fibonacci Sequence

Post by Ani on Wed Mar 04, 2009 6:07 pm

HTang wrote:You swapped the quoted numbers too, which makes the point still valid, as you still end up with -40 as an answer. 40 is the first number, and 0 is the second number.
Ah, good point
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