Câu 13 2.6: Cho chuỗi số sum _(n=1)^+infty sum _(n=1)^sum infty ((-1)^ncdot n^2)/(n^2)+1 Khi đó lim _(narrow infty )u_(n)=? a A B b C ) D 1.

The question asks for the limit of the general term of the series $\sum_{n=1}^{\infty} \frac{(-1)^n n^2}{n^2 + 1}$. Let $u_n = \frac{(-1)^n n^2}{n^2 + 1}$. We want to find $\lim_{n \to \infty} u_n$.<br /><br />As $n$ approaches infinity, the term $\frac{n^2}{n^2 + 1}$ approaches 1. Therefore, we have:<br /><br />$\lim_{n \to \infty} u_n = \lim_{n \to \infty} \frac{(-1)^n n^2}{n^2 + 1} = \lim_{n \to \infty} (-1)^n \cdot \lim_{n \to \infty} \frac{n^2}{n^2 + 1} = \lim_{n \to \infty} (-1)^n \cdot 1 = \lim_{n \to \infty} (-1)^n$<br /><br />The limit $\lim_{n \to \infty} (-1)^n$ does not exist because the sequence $(-1)^n$ oscillates between -1 and 1.<br /><br />Therefore, the limit of the general term $u_n$ does not exist.<br /><br />Final Answer: The final answer is $\boxed{B}$