Determine whether the sequence is divergent or convergent.

Question

If it is convergent, evaluate its limit.
A (sub n)=((4n-7)/(4n+9))

Answer 1

(4n-7)/(4n+9) =

[(4n+9) -16]/(4n+9) =

1 - 16/(4n+9)

The limit thus exists and is equal to 1.

Clearly, for every epsilon > 0, there exists an N such that A_n will be within epsilon of the limiting value for all n > N, taking N = 4/epsilon will do.