Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

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

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!!!: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......

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,614

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.**

Offline

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

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......

Offline

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

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......

Offline

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

May I ask how did you got the answer, we probably used different methods?

psst,

Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,614

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.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

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

Offline

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

that's kool , very KOOL Thank you

psst,

Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......

Offline

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

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)*

Offline

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

Proof:

If *n* is even, the sum is equal to

If

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

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Hi Jane,

JaneFairfax wrote:

Do it this way.

A1: 1

A2: 2

B1: = (-1)^(A1+1)*A1^2Drag 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

Offline