The infinite series a₁ + a₂ + a₃ + …is said to converge if its partial sums converge as a sequence; that is, there exists a limit L such that for all $n>N,\left|{\sum }_{i=1}^n{a}_i-L\right|<\in .$ Note that for a series to converge the sequence made up of its terms must converge to 0, though the converse is not true as demonstrated by the harmonic series.