I got stucked while I was working out whether $\frac{4n-3}{n+43}$ converges. I would be pleased if I could a hint of the above question.
prove that (4n-3)/ (n+43) sequence converges
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real-analysis
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8http://math.stackexchange.com/questions/33970/finding-the-limit-of-fracqnpn-where-q-p-are-polynomials/33971#33971 – 2011-04-29
2 Answers
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Hint: $\frac{4n+3}{n+43} = 4-\frac{175}{n+43} $
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What are the tools that you can use? One possible way is to use Cauchy's theorem: Show that for any given $\varepsilon>0$ there exists $N>0$ such that for all $n>N$ we have $\left|\frac{4n-3}{n+43}-4\right|<\varepsilon$
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1correct answer, but I'd just add that the term "Cauchy's theorem" is non-standard in this context; most people would just say, "by the definition of limits". – 2011-04-29