Convergent Series

An infinite series for which the sequence of partial sums converges. For example, the sequence of partial sums of the series 0.9 + 0.09 + 0.009 + 0.0009 + ··· is 0.9, 0.99, 0.999, 0.9999, .... This sequence converges to 1, so the series 0.9 + 0.09 + 0.009 + 0.0009 + ··· is convergent.