Seeking anwser for a challenging question !!

iamfriendly · 2010-02-14 08:19:46

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

bobbym · 2010-02-14 08:24:53

Hi iamfriendly;

I don't think that is correct, I am getting an answer of - 5050

iamfriendly · 2010-02-14 08:32:47

thank u!!

i will double check but i think i m on the right track

iamfriendly · 2010-02-14 08:34:02

Yep, you are correct, Thank you again!!

iamfriendly · 2010-02-14 08:36:50

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

bobbym · 2010-02-14 08:48:54

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.

phrontister · 2010-02-16 23:58:08

I did it in

and also in .

They were the easy ways for me.

Last edited by phrontister (2010-03-31 22:40:06)

iamfriendly · 2010-03-31 09:21:10

that's kool , very KOOL Thank you

JaneFairfax · 2010-03-31 11:17:13

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)

JaneFairfax · 2010-03-31 11:33:51

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)

phrontister · 2010-03-31 14:37:50

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)

Math Is Fun Forum

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

Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

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

Re: Seeking anwser for a challenging question !!

Board footer