Question

高数大佬求解答

高数大佬求解答高数大佬求答案

Answer 1

lim(n->∞) ∑(k:1->n) (k/n^2)
=lim(n->∞) (1/n)∑(k:1->n) (k/n)
=∫(0->1) x dx
=1/2
lim(n->∞) ∑(k:1->n) (1+ k/n^2)
=lim(n->∞) ∑(k:1->n) (k/n^2) + lim(n->∞) ∑(k:1->n) 1
=1/2 + lim(n->∞) n
->∞

Answer 2

1

追问

过程呢

Answer 3

∑[k=1:n](1+k/n²)
=∑[k=1:n] 1 +∑[k=1:n] k/n²
=n+(1+2+3+…+n)/n²
=n+n(n+1)/2n²
=n+½ (1+1/n)
故lim[n→∞]∑[k=1:n](1+k/n²)
=lim[n→∞]【n+½ (1+1/n)】
=+∞