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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    you can prove that by theorem

  2. anonymous
    • 5 years ago
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    if both ai and bi converge then you can apply the following rule which is what you've done ^_^

  3. anonymous
    • 5 years ago
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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.

  4. anonymous
    • 5 years ago
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    oh okay , you're on the right track so you'll have : (an - bn) where n can be any number :)

  5. anonymous
    • 5 years ago
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    in you case n = m = i :)

  6. anonymous
    • 5 years ago
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    it's a matter of sequence ^_^

  7. anonymous
    • 5 years ago
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    your*

  8. anonymous
    • 5 years ago
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    (a1 + b1 ) - (a2 + b2 ).....(an + bn)

  9. anonymous
    • 5 years ago
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    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

  10. anonymous
    • 5 years ago
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    sure, deviant.g@hotmail.com ^_^ I'll try to help out.

  11. anonymous
    • 5 years ago
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    Thanks I'll send you a scan copy of my work right now

  12. anonymous
    • 5 years ago
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    alright

  13. anonymous
    • 5 years ago
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    your email address did no work here mine tariq_adediran@hotmail.com, so youcan just email me

  14. anonymous
    • 5 years ago
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    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

  15. anonymous
    • 5 years ago
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    1 Attachment
  16. anonymous
    • 5 years ago
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    I still need help

  17. anonymous
    • 5 years ago
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    sklee take the lead?

  18. anonymous
    • 5 years ago
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    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

  19. anonymous
    • 5 years ago
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    teriz, I'm sorry I'm in a hurry, sklee will explain it okay? :)

  20. anonymous
    • 5 years ago
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    That ok thanks anyway

  21. anonymous
    • 5 years ago
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    you're welcome , sklee lead please? ^_^

  22. anonymous
    • 5 years ago
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    sstarica, i will do my best

  23. anonymous
    • 5 years ago
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    awesome, thank you :) I very much appreciate it.

  24. anonymous
    • 5 years ago
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    you're welcome, have a good nite

  25. anonymous
    • 5 years ago
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    lol, it's morning, I'm in campus right now :) thank you

  26. anonymous
    • 5 years ago
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    oops..sorry, where are you at? I mean which country

  27. anonymous
    • 5 years ago
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    Hi Teriz, are you ok with that solution?

  28. anonymous
    • 5 years ago
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    Middle East :), alright gotta finish my assignment now ^_^

  29. anonymous
    • 5 years ago
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    ok, all the best sstarica :)

  30. anonymous
    • 5 years ago
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    thank you ^_^ likewise

  31. anonymous
    • 5 years ago
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    ^_^

  32. anonymous
    • 5 years ago
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    I think so, did you just do the right side?

  33. anonymous
    • 5 years ago
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    oops I mean the left side?

  34. anonymous
    • 5 years ago
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    i started from the left to get the right hand side. I didnt type out the exact right hand side

  35. anonymous
    • 5 years ago
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    ya, i started from the left side

  36. anonymous
    • 5 years ago
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    ok, so will the right side be similar to the left except that when you you combine all the term

  37. anonymous
    • 5 years ago
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    ya, they are the same

  38. anonymous
    • 5 years ago
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    did you understand my teacher email to me because I still was kind of confuse about it?

  39. anonymous
    • 5 years ago
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    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

  40. anonymous
    • 5 years ago
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    which part that you don't understand?

  41. anonymous
    • 5 years ago
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    the left hand, because why is the minus inside for that one, but on the right hand sidethe minus is outside

  42. anonymous
    • 5 years ago
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    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

  43. anonymous
    • 5 years ago
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    So that was basically subtraction prove for the sum sigma notation you gave

  44. anonymous
    • 5 years ago
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    yes

  45. anonymous
    • 5 years ago
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    Sklee is there anyone I can get your email address so I can show you my scan work tommrro

  46. anonymous
    • 5 years ago
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    sklin_04@hotmail.com

  47. anonymous
    • 5 years ago
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    Thanks for all help and by the way what college do you go to?

  48. anonymous
    • 5 years ago
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    i have graduated Teriz

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

  50. anonymous
    • 5 years ago
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    you're welcome,i will do my best

  51. anonymous
    • 5 years ago
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    ok goodnigt

  52. anonymous
    • 5 years ago
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    good nite

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