A series a₁+a₂+…+a_i+…, for which a partial sum S_n=a₁+a₂+…+a_n tends to a finite (or zero) limit as n tends to infinity. This limit is the sum of the series. For example, the series 1+1/2+1/4+1/8+…(with the general term a_i equal to (1/2)ⁱ⁻¹) tends to the limit 2. A series that is not convergent is said to be a divergent series. In such a series the partial sum tends to plus or minus infinity or may oscillate. For example, the series 1+1/2+1/3+1/4+… (with a_i equal to 1/i) is divergent. As can be seen from this latter example, a series may be divergent even if the individual terms a_i tend to zero as i tends to infinity.