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Please help me find limit of the sequence $$ a_n=\frac{n+1}{n+2} $$ and find index $n_0\in\mathbb{N}$ for $\varepsilon=0,01$.

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up vote 3 down vote accepted

$\lim a_n=\lim\frac{n+1}{n+2}=\lim\frac{n(1+\frac{1}{n})}{n(1+\frac{2}{n})}=\frac{1}{1}=1$, because $\lim\frac{1}{n}=0$ and $\lim\frac{2}{n}=0$ if $n\rightarrow\infty$.

Now find $n_0$






Implement the formula: $|\frac{a}{b}|=\frac{|a|}{|b|}$ we have


Because $|-a|=a$, for all $a\in R$, and because $n\in N$ we have:




$n>98$ $\Rightarrow$ $n_0=98$

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