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[tex]Suppose $\lim_n \frac{a_n -1}{a_n +1} = 0$. Prove that $\lim_n a_n = 1$.[/tex]
I am trying to do the algebra so that -a_n < ?? < a_n , but I am having trouble. Am I going about this correctly?
I have also tried to solve each separate side of the inequality. I get a_n < (e+1)/(1-e), but this is not quite fitting.
Can somebody give me a clue please. Thanks
Edit: There is a hint in the book that says to set,
[tex]\(x_{n}=\frac{a_n-1}{a_n+1}\)[/tex] and then solve.
I have done this but I don't know what to do next.
I am trying to do the algebra so that -a_n < ?? < a_n , but I am having trouble. Am I going about this correctly?
I have also tried to solve each separate side of the inequality. I get a_n < (e+1)/(1-e), but this is not quite fitting.
Can somebody give me a clue please. Thanks
Edit: There is a hint in the book that says to set,
[tex]\(x_{n}=\frac{a_n-1}{a_n+1}\)[/tex] and then solve.
I have done this but I don't know what to do next.
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