Definition The infinite series converges and has sum if the sequence of partial sums converges to ,that is .If diverges, then the series diverges. A divergent series has no sum.

• 定义如果级数的部分和数列有极限，即，则称无穷级数收敛，这时极限叫做这级数的和，并写成；如果没有极限，则称无穷级数发散。