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lim(n->oo)[1/n+(n^2)/(n+1)^3+(n^2)/((n+2...

`lim_(n->oo)[1/n+(n^2)/(n+1)^3+(n^2)/((n+2)^3)+......+1/(8n)]`

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lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)] is equal to

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lim_(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)