I need help on proving left side of the subtraction sigma notation to be equal to the right side.
n n n
Σ (ai - bi) = Σ ai - Σ bi
i=m i=m i=m

- anonymous

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- anonymous

you can prove that by theorem

- anonymous

if both ai and bi converge then you can apply the following rule which is what you've done ^_^

- anonymous

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This what the teacher sent, You need to start with one side and end with the other side. It looks like you started with the right hand side and ended with the right hand side. I suggest starting with the left hand side and ending with the right hand side. The first few terms of the left hand side will be: (a1 - b1) + (a2 - b2) + (a3 + b3) +... Start with this and put all the a's together and put all the b's together. Work your algebra magic to get the right hand side of the equation.

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- anonymous

oh okay , you're on the right track so you'll have :
(an - bn) where n can be any number :)

- anonymous

in you case n = m = i :)

- anonymous

it's a matter of sequence ^_^

- anonymous

your*

- anonymous

(a1 + b1 ) - (a2 + b2 ).....(an + bn)

- anonymous

is there anyway to get your email address so I can show you my scan work if it ok with you because it hard to type math work out

- anonymous

sure, deviant.g@hotmail.com ^_^ I'll try to help out.

- anonymous

Thanks I'll send you a scan copy of my work right now

- anonymous

alright

- anonymous

your email address did no work here mine tariq_adediran@hotmail.com, so youcan just email me

- anonymous

This is my work (a1+a2)+.....an-(b1+b2)+.......bin
Which the teacher side that this is the right side and I should sart went the left side and end with the right side

- anonymous

##### 1 Attachment

- anonymous

I still need help

- anonymous

sklee take the lead?

- anonymous

You have \[\sum_{i=m}^{n} a_i - b_i\] on the left hand side, so it is
(a_m - b_m) + (a_(m+1) - b_(m+1)) + ... + (a_(n-1) - b_(n-1)) + (a_n - b_n)
= [a_m + a_(m+1) + ... + a_(n-1) + a_n] - [b_m + b_(m+1) + ... + b_(n-1) + b_n]
= right hand side

- anonymous

teriz, I'm sorry I'm in a hurry, sklee will explain it okay? :)

- anonymous

That ok thanks anyway

- anonymous

you're welcome , sklee lead please? ^_^

- anonymous

sstarica, i will do my best

- anonymous

awesome, thank you :) I very much appreciate it.

- anonymous

you're welcome, have a good nite

- anonymous

lol, it's morning, I'm in campus right now :) thank you

- anonymous

oops..sorry, where are you at? I mean which country

- anonymous

Hi Teriz, are you ok with that solution?

- anonymous

Middle East :), alright gotta finish my assignment now ^_^

- anonymous

ok, all the best sstarica :)

- anonymous

thank you ^_^ likewise

- anonymous

^_^

- anonymous

I think so, did you just do the right side?

- anonymous

oops I mean the left side?

- anonymous

i started from the left to get the right hand side. I didnt type out the exact right hand side

- anonymous

ya, i started from the left side

- anonymous

ok, so will the right side be similar to the left except that when you you combine all the term

- anonymous

ya, they are the same

- anonymous

did you understand my teacher email to me because I still was kind of confuse about it?

- anonymous

just use a simple illustration:
m =1, n = 3
a_1 = 11, a_2 = 12, a_3 = 13; b_1= 1, b_2 = 2, b_3 = 3
The left hand side: (a_1 - b_1) + (a_2 - b_2) + (a_3 - b_3)
= (11-1) + (12-2) + (13-3)
= 10 + 10 + 10 = 30
The right hand side: [a_1 + a_2 + a_3] - [b_1 + b_2 + b_3]
= [11 + 12 + 13] - [1 + 2 + 3]
= 36 - 6 = 30

- anonymous

which part that you don't understand?

- anonymous

the left hand, because why is the minus inside for that one, but on the right hand sidethe minus is outside

- anonymous

The left hand side means you find the difference between respective a and b terms before you sum them. On the right hand side, you sum the a and b terms before you find the difference

- anonymous

So that was basically subtraction prove for the sum sigma notation you gave

- anonymous

yes

- anonymous

Sklee is there anyone I can get your email address so I can show you my scan work tommrro

- anonymous

- anonymous

Thanks for all help and by the way what college do you go to?

- anonymous

i have graduated Teriz

- anonymous

That good, so I'll email you my attached work sometime in the morning or afternoon tomrrow for you to check. Thanks again

- anonymous

you're welcome,i will do my best

- anonymous

ok goodnigt

- anonymous

good nite

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