lim được hiểu là \(\lim\limits_{x\rightarrow\infty}\)
\(\lim\limits_{x\rightarrow\infty}\dfrac{an^2+a^2n+1}{\left(n+1\right)^2}=\lim\limits_{x\rightarrow\infty}\dfrac{an^2+a^2n+1}{n^2+2n+1}=\lim\limits_{x\rightarrow\infty}\dfrac{n^2\left(a+\dfrac{a^2}{n}+\dfrac{1}{n^2}\right)}{n^2\left(1+\dfrac{2}{n}+\dfrac{1}{n^2}\right)}=a\)
Mà \(\lim\limits_{x\rightarrow\infty}\dfrac{a^2n+a^2n+1}{\left(n+1\right)^2}=a^2-a+1\)
\(\Rightarrow a^2-a+1=a\)
\(\Leftrightarrow a^2-2a+1=0\)
\(\Leftrightarrow\left(a-1\right)^2=0\)
\(\Leftrightarrow a=1\)
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