how to finish this proof

[transgalactic]

|(n^2 +10)/(n^3 -10)|<(n^2 +10)/(n^3)< ..<e

i need some (1/n)<e type of equation


??

 

[daon]

Assume n > 2 so that the denominator is positive.

There exists a positive integer C such that n^2+ 10 < C*n^2 for all n.

There exists a positive integer K such that 1/(n^3-10) < K/(n^3) for all n.

So, (n^2+10)/(n^3-10) < (CK)*(1/n)