## 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

1. anonymous

you can prove that by theorem

2. anonymous

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

3. 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.

4. anonymous

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

5. anonymous

in you case n = m = i :)

6. anonymous

it's a matter of sequence ^_^

7. anonymous

your*

8. anonymous

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

9. 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

10. anonymous

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

11. anonymous

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

12. anonymous

alright

13. anonymous

14. 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

15. anonymous

16. anonymous

I still need help

17. anonymous

18. 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

19. anonymous

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

20. anonymous

That ok thanks anyway

21. anonymous

22. anonymous

sstarica, i will do my best

23. anonymous

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

24. anonymous

you're welcome, have a good nite

25. anonymous

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

26. anonymous

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

27. anonymous

Hi Teriz, are you ok with that solution?

28. anonymous

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

29. anonymous

ok, all the best sstarica :)

30. anonymous

thank you ^_^ likewise

31. anonymous

^_^

32. anonymous

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

33. anonymous

oops I mean the left side?

34. anonymous

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

35. anonymous

ya, i started from the left side

36. anonymous

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

37. anonymous

ya, they are the same

38. anonymous

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

39. 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

40. anonymous

which part that you don't understand?

41. anonymous

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

42. 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

43. anonymous

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

44. anonymous

yes

45. anonymous

46. anonymous

sklin_04@hotmail.com

47. anonymous

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

48. anonymous

49. anonymous

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

you're welcome,i will do my best

51. anonymous

ok goodnigt

52. anonymous

good nite