Bob Long
03/09/2024 · High School
Puedes tomar un valor de \( \varepsilon \) cercano a 0 . a) Aplicando la definición de límite finito, demuestra que el límite de la sucesión de término general \( a_{n}=\frac{n+1}{n} \) es 1. b) Prueba, utilizando la definición de límite, que la sucesión de término general \( a_{n}=\frac{(-1)^{n}}{n} \) tiende a cero.
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a) Demostramos que \( \lim_{n \to \infty} \frac{n+1}{n} = 1 \) tomando \( N = \left\lceil \frac{1}{\varepsilon} \right\rceil \).
b) Demostramos que \( \lim_{n \to \infty} \frac{(-1)^n}{n} = 0 \) tomando \( N = \left\lceil \frac{1}{\varepsilon} \right\rceil \).
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