How Can the Sequence (n^2 +10)/(n^3 -10) Be Proven to Converge to 0?

[transgalactic]

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

i need some (1/n)<e


??

 

[rochfor1]

What's the actual question that you're asking?

 

[transgalactic]

i need to prove a convergence

i stuck on the last part
i got

n>10/(e-1)what to write about N ??

 

[JG89]

To show it is bounded:

0 < |(n^2 +10)/(n^3 -10)<2(n^2)/(n^2) = 2

To show it converges, try to show that the sequence is monotone, and use the fact that all bounded and monotonic sequences converge. Or, see below:


To show it converges:

[n^2(1 + 10/n^2)] / [n^2(n - 10/n^2)]

= (1 + 10/n^2) / (n - 10/n^2)

the 10/n^2 in both the numerator and denominator converge to 0 and so we have 1/n, which converges to 0 as well.