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#1 2010-02-15 07:19:46
- iamfriendly
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Seeking anwser for a challenging question !!
Here is the question:
what is the difference for the equation of "square of 1 - square of 2 + square of 3 - square of 4........+ square of 99 - square of 100"?
I got -5500, is that correct?
Please give any assitance!
Thank you for helping!!!
EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......
#2 2010-02-15 07:24:53
- bobbym
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Re: Seeking anwser for a challenging question !!
Hi iamfriendly;
I don't think that is correct, I am getting an answer of - 5050
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#3 2010-02-15 07:32:47
- iamfriendly
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Re: Seeking anwser for a challenging question !!
thank u!!
i will double check but i think i m on the right track
EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......
#4 2010-02-15 07:34:02
- iamfriendly
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Re: Seeking anwser for a challenging question !!
Yep, you are correct, Thank you again!!
EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......
#5 2010-02-15 07:36:50
- iamfriendly
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Re: Seeking anwser for a challenging question !!
May I ask how did you got the answer, we probably used different methods?
EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......
#6 2010-02-15 07:48:54
- bobbym
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Re: Seeking anwser for a challenging question !!
Hi;
Of course you can ask. I do it the easy way.
There are 2 ways I work that type of problem when I need a quick rough and tumble answer.
!) I take it to wolfram alpha, a site that is available to everyone. It immediately provides the -5050 result.
2) I look it up in a table of sums that was provided to me when I needed them on a daily basis for problems.
Then just substitute in for n = 100 to get -5050.
Actually to do it analytically is not difficult at all, you can try differences and a generating function. Proving that your answer is correct would probably involve induction.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#7 2010-02-17 22:58:08
- phrontister
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Re: Seeking anwser for a challenging question !!
I did it in and also in .
They were the easy ways for me.
Last edited by phrontister (2010-04-01 21:40:06)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#8 2010-04-01 08:21:10
- iamfriendly
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Re: Seeking anwser for a challenging question !!
that's kool , very KOOL Thank you
EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......
#9 2010-04-01 10:17:13
- JaneFairfax
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Re: Seeking anwser for a challenging question !!
phrontister wrote:
Do it this way.
A1: 1
A2: 2
B1: 
-1)^(A1+1)*A1^2
Drag copy handle on cell B1 down to B2. Then select the four cells A1:B2 and drag copy handle down to row 100.
Then enter this:
B101: =SUM(B1:B100)
Last edited by JaneFairfax (2010-04-01 21:50:05)
#10 2010-04-01 10:33:51
- JaneFairfax
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Re: Seeking anwser for a challenging question !!
Proof:
If n is even, the sum is equal to
If n is odd, evaluate the sum to n−1 (which is even) and add n2.
Last edited by JaneFairfax (2010-04-01 10:42:42)
#11 2010-04-01 13:37:50
- phrontister
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Re: Seeking anwser for a challenging question !!
Hi Jane,
JaneFairfax wrote:
Do it this way.
A1: 1
A2: 2
B1: = (-1)^(A1+1)*A1^2
Drag copy handle on cell B1 down to B2. Then select the four cells A1:B2 and drag copy handle down to row 100.
Then enter this:
B101: =SUM(B1:B100)
Nice! 
Much more streamlined than mine...which now looks rather clumsy.
Just a couple of things:
1. More streamlining:
A1: 1
B1: = (-1)^(A1+1)*A1^2
Select these two cells and drag copy handle them down to row 100.
B101: =SUM(B1:B100)
Your formula obviates the need for multiple-row selection.
2. An alternative:
A1: 1
A2: 2
B1: A1^2
B2: -(A2^2)
Select the four cells A1:B2 and drag copy handle them down to row 100.
B101: =SUM(B1:B100)
This alternative utilises the way Excel and OOoCalc paste a 'drag copy' of a multiple-row selection.
Last edited by phrontister (2010-04-02 10:43:55)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson