Prove that ` lim_(n rarr oo)[(1^(2)+2^(2)+3^(2)+cdots+n^(2))/(n^(3))]=(1)/(3)`

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1. lim_(n rarr oo)(n+n^(2)+n^(3)+...*n^(n))/(1^(n)+1^(n)+3^(n)+cdots+n^(n))