If the nth partial sum of an infinite series is Sn = (5n^2 -4) / (n^2 +5), what is the sum of the series?

The sum of an infinite series is the limit of the sequence of partial sums. So, all you need to do is determine the limit, as n approaches infinity, of (5n^2 - 4) / (n^2 + 5). But this is easy; the expression evaluates to infinity over infinity, so you can use L'Hopital's rule. Taking the derivative of both the numerator and the denominator, you get 10n / 2n, which reduces to 5. So the limit of the sequence of partial sums is 5, meaning that the series sums to be 5.