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    if you have a sequence a_n and a sequence b_n, is there such a sequence a_n+b_n? I think there is, but i am not sure
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    (Original post by asdfyolo)
    if you have a sequence a_n and a sequence b_n, is there such a sequence a_n+b_n? I think there is, but i am not sure
    You can certainly create such a sequence by adding corresponding terms, or you could multiply them to get a sequence (a_nb_n), or take any function of the two (f(a_n,b_n)) as long as (a_n)\text{ and }(b_n) are in the domain of f.
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    (Original post by ghostwalker)
    You can certainly create such a sequence by adding corresponding terms, or you could multiply them to get a sequence (a_nb_n), or take any function of the two (f(a_n,b_n)) as long as (a_n)\text{ and }(b_n) are in the domain of f.
    thanks. does that have anything to do with answering this: suppose a_n \leq b_n and the limit of the first sequence is a, and the limit of the second sequence is b, show a \leq b.i have been told it has something to do with showing a-b \leq z for all z>0
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    (Original post by asdfyolo)
    thanks. does that have anything to do with answering this: suppose a_n \leq b_n and the limit of the first sequence is a, and the limit of the second sequence is b, show a \leq b.i have been told it has something to do with showing a-b \leq z for all z>0
    Told by whom. Seems an odd inequality, when you could just show a-b <= 0. Not sure how they're envisioning you do it with going for that inequality.

    Also going to depend on what you've covered already regarding the limit of the sum/difference of two sequences.

    And I'm a bit puzzled why you were asking about a_n + b_n, since that doesn't come into it.


    I'd go for a proof by contradiction myself.
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    (Original post by ghostwalker)
    Told by whom. Seems an odd inequality, when you could just show a-b <= 0. Not sure how they're envisioning you do it with going for that inequality.

    Also going to depend on what you've covered already regarding the limit of the sum/difference of two sequences.

    And I'm a bit puzzled why you were asking about a_n + b_n, since that doesn't come into it.


    I'd go for a proof by contradiction myself.
    told by a lecturer, we have covered the limit of the sum of two sequences (i just found out now), i have to do it that weird way
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    (Original post by asdfyolo)
    told by a lecturer, we have covered the limit of the sum of two sequences (i just found out now), i have to do it that weird way
    OK.

    Now that I look at it again, it's not that bad.

    If we let b_n-a_n=c_n which is >= 0.

    We have b_n=a_n +c_n

    and now consider the limits.

    I presume you can assume the limit of a positive sequence is >= 0.
 
 
 
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