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

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

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S1: lim_(n->oo) (2^n + (-2)^n)/2^n does not exist S2: lim_(n->oo) (3^n + (-3)^n)/4^n does not exist

Evaluate: lim_(n rarr oo)(1^(2)+2^(2)+......+n^(2))/(n^(3))

Evaluate: lim_(n rarr oo)(1^(2)+2^(2)+......+n^(2))/(n^(3))

lim_(n to oo) (1^(2)+2^(2)+3^(2)+…+n^(2))/(n^(3)) is equal to

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

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

Prove that lim_ (n rarr oo) ((1 ^ (2)) / (n ^ (3)) + (2 ^ (2)) / (n ^ (3)) + (3 ^ (2)) / ( n ^ (3)) + .... + (n ^ (2)) / (n ^ (3))) = (1) / (3)

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

lim_(n rarr oo)(1^(2)+2^(2)+3^(2)+.........+n^(2))/(n^(3)) is equal to -

lim (n rarr oo) (1 ^ (2) + 2 ^ (2) + 3 ^ (3) + ......... + n ^ (2)) / (n ^ (3))