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#1 2010-02-14 08:19:46

iamfriendly
Member
Registered: 2009-07-03
Posts: 72

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?dunno

Please give any assitance!

Thank you for helping!!!:D


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......

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#2 2010-02-14 08:24:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2010-02-14 08:32:47

iamfriendly
Member
Registered: 2009-07-03
Posts: 72

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......

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#4 2010-02-14 08:34:02

iamfriendly
Member
Registered: 2009-07-03
Posts: 72

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......

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#5 2010-02-14 08:36:50

iamfriendly
Member
Registered: 2009-07-03
Posts: 72

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......

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#6 2010-02-14 08:48:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2010-02-16 23:58:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,928

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 (2010-03-31 22:40:06)


"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

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#8 2010-03-31 09:21:10

iamfriendly
Member
Registered: 2009-07-03
Posts: 72

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......

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#9 2010-03-31 11:17:13

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Seeking anwser for a challenging question !!

phrontister wrote:

Do it this way.

A1: 1
A2: 2
B1: sad-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 (2010-03-31 22:50:05)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#10 2010-03-31 11:33:51

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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 n[sup]2[/sup].
­

Last edited by JaneFairfax (2010-03-31 11:42:42)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#11 2010-03-31 14:37:50

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,928

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! smile 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 (2010-04-01 11:43:55)


"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

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