数列极限题⊙▽⊙
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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
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.