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[" The value of "],[[,lim(n rarr oo)(1+2...

[" The value of "],[[,lim_(n rarr oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))-lim_(n rarr oo)(1+2^(3)+3^(3)+...+n^(3))/(n^(5))],[" is "," (a) zero "(b)1/4," (c) "1/5quad " (d) "1/30]]

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The value of [lim_(n to oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))-lim_(n to oo)(1+2^(3)+3^(3)+...+n^(3))/(n^(5))] is equal to -

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

{:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "Lt),(n rarr oo):} ((1+2^(3)+3^(3)+....+n^(3))/(n^(5)))=

The value of lim_(n rarr oo)(1/(1-n^4)+8/(1-n^4)+...+n^3/(1-n^4)) is

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

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