收敛数列的有界性问题设数列{Xn}有界,又lim Yn=0,证明：lim XnYn=0.囧么办?111_数学解答

收敛数列的有界性问题
设数列{Xn}有界,又lim Yn=0,证明：lim XnYn=0.囧么办?111

人气：235 ℃　时间：2020-03-24 20:09:14

解答

|xn|≤M
-Myn≤xn.yn≤Myn
-Mlim(n->∞)yn≤lim(n->∞)xn.yn≤Mlim(n->∞)yn
0 ≤lim(n->∞)xn.yn≤0
=>lim(n->∞)xn.yn =0