Question

z

請幫忙詳解求求了
急！

2
1² +2² +...+n²
(2) lim
818
n² + 2n³/h (n+1) |

Answer 1

✨ 最佳解答 ✨

qn

連續正整數平方和
1²+2²+3²+ ⋯ + n² = n(n+1)(2n+1)/6

lim_{n→∞} [ n(n+1)(2n+1) / 6(n²+2n³) ]
= lim_{n→∞} [ (2n³+3n²+n)/(12n³+6n²) ]
(上下同除以 n³)
= lim_{n→∞} [ (2 + 3/n + 1/n²) / (12 + 6/n) ]
= (2 + 0 + 0) / (12 + 0)
= 1/6