# How to finish this proof

1. Dec 2, 2008

### transgalactic

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

i need some (1/n)<e

??

2. Dec 2, 2008

### rochfor1

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

3. Dec 2, 2008

### transgalactic

i need to prove a convergence

i stuck on the last part
i got

n>10/(e-1)

what to write about N ??

4. Dec 2, 2008

### 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.

Last edited: Dec 2, 2008