Re: [考古] 97台大商研(極限)
※ 引述《evelynsue (Evelyn)》之銘言：
: _____
: l i m √n^2+n - n = ?
: n →∞
lim √(n^2 + n) - n
n→∞
(√(n^2 + n) - n)(√(n^2 + n) + n)
= lim ----------------------------------
n→∞ √(n^2 + n) + n
(n^2 + n) - n^2
= lim -------------------
n→∞ √(n^2 + n) + n
n
= lim -----------------
n→∞ √(n^2 + n) + n
1 1 1
= lim ------------------- = ------- = ---
n→∞ √(1 + (1/n)) + 1 1 + 1 2
--
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