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amyna
 one year ago
find the limit of the sequence
n1/n
amyna
 one year ago
find the limit of the sequence n1/n

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amyna
 one year ago
Best ResponseYou've already chosen the best response.0you take the limit as n approaches infinity

amyna
 one year ago
Best ResponseYou've already chosen the best response.0but i don't know how to start

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Is it \(\large\rm \frac{n1}{n}\) or \(\large\rm n\frac{1}{n}\) ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Oh limit of the sequence? not the series? Ok that makes things a little easier then :d

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \lim_{n\to\infty}\frac{n1}{n}\quad=\quad \lim_{n\to\infty}\frac{n}{n}\frac{1}{n}\quad=\quad \lim_{n\to\infty}1\lim_{n\to\infty}\frac{1}{n}\]You could break it up like this I suppose. That seems like a good start :o

amyna
 one year ago
Best ResponseYou've already chosen the best response.0ok i will try this approach, can i also multiply both sides by n ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2No no let's not try anything fancy like that :) We don't actually have any "sides" here. It's just this guy \(\large\rm \lim\limits_{n\to\infty}\frac{n1}{n}\) and we're rewriting him in a way that's easier to handle. Our limit depends on n, So in the same way that you can't factor n `out of the limit`, Example:\(\large\rm \lim\limits_{n\to\infty}2\frac{1}{n}\ne\frac{1}{n}\lim\limits_{n\to\infty}\frac{1}{n}2\) (Can't pull the n stuff out like that) we also don't want to introduce new n stuff into the limit! :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Ah typo in my example :c woops

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2I was trying to say that you can't factor the 1/n outside of the limit. Was just trying to give an example why you don't want to multiply any n's into the limit.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm =\quad \lim_{n\to\infty}1\lim_{n\to\infty}\frac{1}{n}\]But if we were able to break it down into these two limits, these should be manageable. You don't remember that second limit? :o

amyna
 one year ago
Best ResponseYou've already chosen the best response.0then how would i solve it after i break the function up? sorry it has been long since i learned limits so i don't really remember how to actually solve it.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2I applied a limit rule to break it into two separate limits. As `n approaches infinity`, what does the number 1 approach?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2careful! we're not adding up a bunch of 1's. We're just looking at that number 1 as n grows and grows. 1 is a constant. It's unchanging. So as n gets larger and larger, 1 approaches 1. Hopefully that makes some sense :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2But for the other part... As `n approaches infinity`... let's look at a really big n to see what's going on.\[\large\rm \lim_{n\to\infty}\frac{1}{n}\approx\frac{1}{12bajillion}\]I plugged in a really really big number for n, letting it get "close" to infinity.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2This is one of those limits that you really want to remember :) But oh well hehe. So do you notice anything about this number? How about a number you can plug into your calculator, like 1/99999?

amyna
 one year ago
Best ResponseYou've already chosen the best response.0so how would i show the necessary work for this problem since it approaches 1?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2You do these simple algebra steps,\[\large\rm \lim_{n\to\infty}\frac{n1}{n}\quad=\quad \lim_{n\to\infty}\frac{n}{n}\frac{1}{n}\quad=\quad \lim_{n\to\infty}1\frac{1}{n}\]And then, at this point in your class, your teacher probably wants you to state what rule you're using here. \[\large\rm =\lim_{n\to\infty}1\lim_{n\to\infty}\frac{1}{n}\]Justify that step by saying something like... `The limit of a difference is equivalent to the difference of limits`. Or whatever the name of that limit rule is, I can't remember. \[\large\rm =10\]\[\large\rm =1\]I think that's all you need to do :o I don't think you need to say anything special about the 1/n limit. That's a pretty common one. I could be wrong though.

amyna
 one year ago
Best ResponseYou've already chosen the best response.0Okay this makes so much more sense now! Thank You for your help!
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