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111香山高中

11.
試問\(\displaystyle \lim_{n\to \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\ldots+\frac{1}{\sqrt{n}}\right)=\)?
(A)0 (B)1 (C)2 (D)3 (E)4
我的教甄準備之路 黎曼和和夾擠定理,https://math.pro/db/viewthread.php?tid=661&page=3#pid23615

13.
設\(n\)為正整數,如果二次函數\( y=8^nx^2-2^n(2^n+1)x+1 \)的圖形與\(x\)軸交於二點\( A_n \)、\( B_n \),令線段\( \overline{A_nB_n} \)之長為\( L_n \),則\( \displaystyle \sum_{n=1}^{\infty}L_n= \)?
(A)\(\displaystyle \frac{1}{4}\) (B)\(\displaystyle \frac{1}{3}\) (C)\(\displaystyle \frac{1}{2}\) (D)\(\displaystyle \frac{2}{3}\) (E)\(\displaystyle \frac{3}{4}\)

設\( y=8^nx^2-2^n(2^n+1)x+1 \)( \( n \in N \) )之圖形與\(x\)軸交於\( A_n \)與\( B_n \)兩點,若\( \overline{A_nB_n} \)之長為\( l_n \),則\( \displaystyle \sum_{n=1}^{\infty}l_n \)之和為?
(101台中女中,https://math.pro/db/viewthread.php?tid=1327&page=2#pid5463)
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