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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?

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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

### 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: -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)

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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)

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

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

### 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 (2010-04-01 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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