Question

limx趋向无穷时,√n∧2＋n－n的极限是多少

Answer 1

limn->∞ √(n^2+n) -n =limn->∞ [√(n^2+n) -n][√(n^2+n) +n] / [√(n^2+n) +n] =limn->∞ (n^2+n-n^2) / n [√(1+1/n) +1] =limn->∞ n / n [√(1+1/n) +1] =limn->∞ 1/[√(1+1/n) +1] =1/(1+1) =1/2