Question

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

Answer 1

you can prove that by theorem

Answer 2

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

Answer 3

.
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.

Answer 4

oh okay , you're on the right track so you'll have :

(an - bn) where n can be any number :)

Answer 5

in you case n = m = i :)

Answer 6

it's a matter of sequence ^_^

Answer 7

your*

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

alright

Answer 13

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

Answer 14

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

Answer 15

I still need help

Answer 16

sklee take the lead?

Answer 17

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

Answer 18

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

Answer 19

That ok thanks anyway

Answer 20

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

Answer 21

sstarica, i will do my best

Answer 22

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

Answer 23

you're welcome, have a good nite

Answer 24

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

Answer 25

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

Answer 26

Hi Teriz, are you ok with that solution?

Answer 27

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

Answer 28

ok, all the best sstarica :)

Answer 29

thank you ^_^ likewise

Answer 30

^_^

Answer 31

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

Answer 32

oops I mean the left side?

Answer 33

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

Answer 34

ya, i started from the left side

Answer 35

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

Answer 36

ya, they are the same

Answer 37

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

Answer 38

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

Answer 39

which part that you don't understand?

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

yes

Answer 44

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

Answer 45

sklin_04@hotmail.com

Answer 46

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

Answer 47

i have graduated Teriz

Answer 48

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

Answer 49

you're welcome,i will do my best

Answer 50

ok goodnigt

Answer 51

good nite