Question

求一道极限

求一道极限如图拜托31 32两道题目

Answer 1

(31)
S = 1/(n^2+n+1) + 2/(n^2+n+2)+....+n/(n^2+n+n)
S≤ 1/(n^2+n+1) + 2/(n^2+n+1)+....+n/(n^2+n+1) = [n(n+1)/2 ]/(n^2+n+1)
lim(n->∞) [n(n+1)/2 ]/(n^2+n+1) = 1/2
/
S≥1/(n^2+n+n) + 2/(n^2+n+n)+....+n/(n^2+n+n) = [n(n+1)/2 ]/(n^2+n+n)
lim(n->∞) [n(n+1)/2 ]/(n^2+n+n) = 1/2
=>
lim(n->∞) [ 1/(n^2+n+1) + 2/(n^2+n+2)+....+n/(n^2+n+n) ] = 1/2
(32)
lim(x->∞ ) (x+1)^95.(ax+1)^5 /(x^2+1)^50 =8
分子，分母同时除以 x^100
lim(x->∞ ) (1+1/x)^95.(a+1/x)^5 /(1+1/x^2)^50 =8
a^5 =8
a = 8^(1/5)=2^(3/5)

追问

大佬能不能写纸上这个密密麻麻的我看不进去啊