Question

求解图上的题目！第五题最好写过程

Answer 1

3. (n-1)^22 = n^22 + o(N), (2n-1)^2 = 4n^2 + o(N), (n-3)^20 = n^20 + o(n), lim = ¼
4.
n^2 / (an+b) – n^3/(2n^2-1) = 2n^4 – n^2 – an^4 – bn^3)/(2n^2 - 1)(an+b)
分母=2a n^3 + o(n)
分子= （2-a）n^4 – bn^3 +o(n)
所以a = 2, b/2a = -1/4, b = -2a/4 = -1
a = 2, b = -1
5.
k/n 分成k 个1/n
1/n – 1/(n+1) = 1/(n(n+1))
1/n – 1/(n+2) = 2/(n(n+2))
…
1/n – 1/(n+k) = k/(n(n+k))
Lim = lim n^2 / (n(n+1)) +2 lim n^2 / (n(n+k)) …
= 1 + 2 + 3… + k = (k+1)k/2