Calculus 1 do the following sequence go to infinity?

Question

Does the following sequence go to infinity?

a)n^2-4n+6/n^3+n+3

Answer 1

Assuming you mean that the nth term in the sequence is:

S(n) = (n^2 - 4n + 6) / (n^3 + n + 3),

Then, as n tends towards infinity, the numerator tends towards n^2 (the -4n + 6 is small compared to the n^2) and the denominator tends towards n^3 (the n + 3 is small compared to n^3). Thus, as n-> infinity,

S(n) -> n^2 / n^3 = 1 / n -> 0

Thus, the sequence tends towards zero as n -> infinity.