Calcular o limite da sucessão [tex]lim(\frac{1}{n^{2}}+\frac{2}{n^{2}}+\frac{n}{n^{2}})[/tex]
05 abr 2016, 23:55
\(lim(\frac{1}{n^{2}}+\frac{2}{n^{2}}+\frac{n}{n^{2}})\)
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Re: Calcular o limite da sucessão [tex]lim(\frac{1}{n^{2}}+\frac{2}{n^{2}}+\frac{n}{n^{2}})[/tex]
06 abr 2016, 03:14
Boa noite!
\(\lim_{n\to\infty}\left(\frac{1}{n^2}+\frac{2}{n^2}+\ldots+\frac{n}{n^2}\right)
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(1+2+\ldots+n\right)\right]
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(\frac{(1+n)n}{2}\right)\right]
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(\frac{n+n^2}{2}\right)\right]
\lim_{n\to\infty}\left(\frac{\frac{1}{n}+1}{2}\right)=\frac{1}{2}\)
Espero ter ajudado!
\(\lim_{n\to\infty}\left(\frac{1}{n^2}+\frac{2}{n^2}+\ldots+\frac{n}{n^2}\right)
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(1+2+\ldots+n\right)\right]
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(\frac{(1+n)n}{2}\right)\right]
\lim_{n\to\infty}\left[\frac{1}{n^2}\cdot\left(\frac{n+n^2}{2}\right)\right]
\lim_{n\to\infty}\left(\frac{\frac{1}{n}+1}{2}\right)=\frac{1}{2}\)
Espero ter ajudado!