|(n^2 +10)/(n^3 -10)<(n^2 +10)/(n^3)< ..<e
i need some (1/n)<e
What's the actual question that you're asking?
i need to prove a convergence
i stuck on the last part
what to write about N ??
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.
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