Hi(adsbygoogle = window.adsbygoogle || []).push({});

with having the sentence bellow:

«A number b is called the limit of a sequence [tex] x_{1}, x_{2}, . . . , x_{n}, . . . [/tex] if for any [tex] \epsilon > 0 [/tex] there is

[tex] N = N(\epsilon) [/tex] such that [tex] |x_{n}[/tex]– [tex] b| < \epsilon [/tex] for all n > N.»

I have a question.does the N mean the number of sentence?

If yes could you explain me this example?

«Let us show that [tex] \lim_{n \rightarrow \infty}=\frac{n}{n+1}=1 [/tex] .

Consider the difference [tex] |\frac{n}{n+1}-1|=\frac{1}{n+1} [/tex] .The inequality [tex] \frac{1}{n+1}<\epsilon [/tex] holds for all [tex] n>\frac{1}{\epsilon}-1=N(\epsilon) [/tex] .

Therefore,for any positive [tex] \epsilon [/tex] there is [tex] N=\frac{1}{\epsilon}-1 [/tex] such that for n>N we have [tex] |\frac{n}{n+1}-1|<\epsilon [/tex] .»

Because I solved the equation [tex] x_{n}=\frac{n}{n+1} [/tex] due to n and I found [tex] n=\frac{x_{n}}{x_{n}+1} [/tex] but [tex] N=\frac{1 - x_{n}}{x_{n}} [/tex]

What is the problem?

And when I tried to use $ instead of [/tex] and [tex],In preview it didn't work and showed the exact code.

And typing - caused «8211;».

thanks

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# My problem from a text about limit of a sequence

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