anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you can prove that by theorem
anonymous
  • anonymous
if both ai and bi converge then you can apply the following rule which is what you've done ^_^
anonymous
  • anonymous
. 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
  • anonymous
oh okay , you're on the right track so you'll have : (an - bn) where n can be any number :)
anonymous
  • anonymous
in you case n = m = i :)
anonymous
  • anonymous
it's a matter of sequence ^_^
anonymous
  • anonymous
your*
anonymous
  • anonymous
(a1 + b1 ) - (a2 + b2 ).....(an + bn)
anonymous
  • 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
  • anonymous
sure, deviant.g@hotmail.com ^_^ I'll try to help out.
anonymous
  • anonymous
Thanks I'll send you a scan copy of my work right now
anonymous
  • anonymous
alright
anonymous
  • anonymous
your email address did no work here mine tariq_adediran@hotmail.com, so youcan just email me
anonymous
  • 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
  • anonymous
1 Attachment
anonymous
  • anonymous
I still need help
anonymous
  • anonymous
sklee take the lead?
anonymous
  • 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
  • anonymous
teriz, I'm sorry I'm in a hurry, sklee will explain it okay? :)
anonymous
  • anonymous
That ok thanks anyway
anonymous
  • anonymous
you're welcome , sklee lead please? ^_^
anonymous
  • anonymous
sstarica, i will do my best
anonymous
  • anonymous
awesome, thank you :) I very much appreciate it.
anonymous
  • anonymous
you're welcome, have a good nite
anonymous
  • anonymous
lol, it's morning, I'm in campus right now :) thank you
anonymous
  • anonymous
oops..sorry, where are you at? I mean which country
anonymous
  • anonymous
Hi Teriz, are you ok with that solution?
anonymous
  • anonymous
Middle East :), alright gotta finish my assignment now ^_^
anonymous
  • anonymous
ok, all the best sstarica :)
anonymous
  • anonymous
thank you ^_^ likewise
anonymous
  • anonymous
^_^
anonymous
  • anonymous
I think so, did you just do the right side?
anonymous
  • anonymous
oops I mean the left side?
anonymous
  • anonymous
i started from the left to get the right hand side. I didnt type out the exact right hand side
anonymous
  • anonymous
ya, i started from the left side
anonymous
  • anonymous
ok, so will the right side be similar to the left except that when you you combine all the term
anonymous
  • anonymous
ya, they are the same
anonymous
  • anonymous
did you understand my teacher email to me because I still was kind of confuse about it?
anonymous
  • 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
  • anonymous
which part that you don't understand?
anonymous
  • anonymous
the left hand, because why is the minus inside for that one, but on the right hand sidethe minus is outside
anonymous
  • 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
  • anonymous
So that was basically subtraction prove for the sum sigma notation you gave
anonymous
  • anonymous
yes
anonymous
  • anonymous
Sklee is there anyone I can get your email address so I can show you my scan work tommrro
anonymous
  • anonymous
anonymous
  • anonymous
Thanks for all help and by the way what college do you go to?
anonymous
  • anonymous
i have graduated Teriz
anonymous
  • 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
  • anonymous
you're welcome,i will do my best
anonymous
  • anonymous
ok goodnigt
anonymous
  • anonymous
good nite

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