数列极限题⊙▽⊙
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 20:38:26
![数列极限题⊙▽⊙](/uploads/image/z/2688679-55-9.jpg?t=%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E9%A2%98%E2%8A%99%E2%96%BD%E2%8A%99)
数列极限题⊙▽⊙
数列极限题⊙▽⊙
数列极限题⊙▽⊙
证明:∵0≤│n^(2/3)sinn/(n+1)│≤n^(2/3)/(n+1)
又lim(n->∞)[n^(2/3)/(n+1)]=lim(n->∞)[(1/n^(1/3))/(1+1/n)]=0/(1+0)=0
∴0=lim(n->∞)[n^(2/3)sinn/(n+1)]=lim(n->∞)[n^(2/3)/(n+1)]=0
故lim(n->∞)[n^(2/3)sinn/(n+1)]=0,证毕.