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# sequences watch

1. if you have a sequence and a sequence , is there such a sequence ? I think there is, but i am not sure
2. (Original post by asdfyolo)
if you have a sequence and a sequence , is there such a sequence ? 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 , or take any function of the two as long as are in the domain of f.
3. (Original post by ghostwalker)
You can certainly create such a sequence by adding corresponding terms, or you could multiply them to get a sequence , or take any function of the two as long as are in the domain of f.
thanks. does that have anything to do with answering this: suppose and the limit of the first sequence is a, and the limit of the second sequence is b, show .i have been told it has something to do with showing for all z>0
4. (Original post by asdfyolo)
thanks. does that have anything to do with answering this: suppose and the limit of the first sequence is a, and the limit of the second sequence is b, show .i have been told it has something to do with showing 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.
5. (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
6. (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 which is >= 0.

We have

and now consider the limits.

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

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