why that limit is 1?

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Calado99

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I don't know how lim(1+2/n)3 is 1
 

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I have to say that I do not understand it either.

[MATH]\lim_{n \rightarrow 2} \left ( \dfrac{n + 2}{n} \right )^{(n+3)} = 32 \ne e^2.[/MATH]
But, you object, they did not say that was the limit when n was approaching 2. True. They did not specify a specific target, which must mean that it is true for all targets, which must mean it is true for 2. I say they are wrong.
 
JeffM said:
I have to say that I do not understand it either.

[MATH]\lim_{n \rightarrow 2} \left ( \dfrac{n + 2}{n} \right )^{(n+3)} = 32 \ne e^2.[/MATH]
But, you object, they did not say that was the limit when n was approaching 2. True. They did not specify a specific target, which must mean that it is true for all targets, which must mean it is true for 2. I say they are wrong.
Click to expand...


There is not a limit as n approaches 2 in the problem there. I would like there to be an explicit limit as n going to oo, but I understand that the way this is written, that implies that. If so, the supposed answer of e^2 is correct.
 
JeffM said:
I have to say that I do not understand it either.

[MATH]\lim_{n \rightarrow 2} \left ( \dfrac{n + 2}{n} \right )^{(n+3)} = 32 \ne e^2.[/MATH]
But, you object, they did not say that was the limit when n was approaching 2. True. They did not specify a specific target, which must mean that it is true for all targets, which must mean it is true for 2. I say they are wrong.
Click to expand...
The way I read it, they are learning about sequences, in which context all limits are as n approaches infinity.

I'd rather that were stated explicitly, as otherwise an inadequate notation is being taught; but it can be understood, and I chose to do so.
 
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