Math Is Fun Forum

kathreen

Guest

sigma

whats the value of this sigma :

1 ² - 2 ² + 3 ² - 4 ² + 5 ² - 6 ² + ... +199 ²

i really worked trying to solve it ... but all the doors were closed i tried to divide it into two and get they sigma of each one so the total is the answer but no way ...

who can help me or at least give me the idea and i'll be grateful

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: sigma

Last edited by luca-deltodesco (2007-02-27 07:38:18)

---

The Beginning Of All Things To End.
The End Of All Things To Come.

kathreen

Guest

Re: sigma

luca-deltodesco thanks but i didnt get it ... can you explain more ?! with number if you dont mind

jane dont forget that we have positive and negative numbers so ...

kathreen

Guest

Re: sigma

thanks luca i think i got it ! thanks alot

kathreen

Guest

Re: sigma

i got the way but how to do it ?! sorry

kathreen

Guest

Re: sigma

maybe you can split that sum into two sums: 'i' odd and 'i' even. Then you just have to sum two expressions not involving (-1)^i-1

i thought about it but i got some difficulity to write that in sigma ... can you help ?!

Sekky

Member

Registered: 2007-01-12

Posts: 181

Re: sigma

maybe you can split that sum into two sums: 'i' odd and 'i' even. Then you just have to sum two expressions not involving (-1)^i-1

Like sigma i=1 to 99 of some function of 2i plus i from 1 to 100 of some function of 2i+1 (possibly reversed I can't care enough to think about it)

Nah, delta's way is far superior.

But change i-1 for i+1....for the sake of sake's sake.

kathreen

Guest

Re: sigma

aha thanks sekky for saying that but its really hard for me to get out that in this way :

199
∑     = ( -1 ) ^ ( i + 1 ) × i ²
i=1

could you help me please ?!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: sigma

Pairing up terms might well help you. (n+1)² - n² = 2n+1, so by pairing up consecutive terms (you can pair the first one with 0² without changing the result) you can simplify the summation quite a bit.

---

Why did the vector cross the road?
It wanted to be normal.

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

Re: sigma

you can write it like this :
(1 ² - 2 ²) + (3 ² - 4 ² ) + ( 5 ² - 6 ²) + ... +199 ²
-3 + - 7 + - 11 + ...

its a series now

or you can do it with sigma like this :

---

ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...