Question

How do I take the limit as n goes to infinity of (1/2)/(2n-3)

Answer 1

It would be zero because the infinity would be in the denominator.

Answer 2

you can tell that for arbitrarily large values of n, this term gets arbitrarily close to 0, so you can say that the limit as n approaches infinity of this is 0. if you want something more rigorous you can try an epsilon delta proof to show that: (for all)(epsilon > 0)(there exists)(N) such that if n >= N then |(1/2)/(2n -3)| < (epsilon)