other types of sequences that are easy to define include: An integer sequence is a sequence whose terms are integers. A polynomial sequence is a sequence whose terms are polynomials. A positive integer sequence is sometimes called multiplicative, if anm = an am for all pairs n, m such that n and m are coprime. In other instances, sequences are often called multiplicative, if an = na1 for all n. Moreover, a multiplicative Fibonacci sequence satisfies the recursion relation an = an−1 an−2. A binary sequence is a sequence whose terms have one of two discrete values, e.g. base 2 values (0,1,1,0, ...), a series of coin tosses (Heads/Tails) H,T,H,H,T, ..., the answers to a set of True or False questions (T, F, T, T, ...), and so on. Limits and convergence An important property of a sequence is convergence. If a sequence converges, it converges to a particular value known as the limit. If a sequence converges to some limit, then it is convergent. A sequence that does not converge is divergent. Informally, a sequence has a limit if the elements of the sequence become closer and closer to some value (called the limit of the sequence), and they become and remain arbitrarily close to , meaning that given a real number greater than zero, all but a finite number of the elements of the sequence have a distance from less than . For example, the sequence shown to the right converges to the value 0. On the other hand, the sequences (which begins 1, 8, 27, …) and (which begins −1, 1, −1, 1, …) are both divergent. If a sequence converges, then the value it converges to is unique. This value is called the limit of the sequence. The limit of a convergent sequence is normally denoted . If is a divergent sequence, then the expression is meaningless. Formal definition of convergence A sequence of real numbers converges to a real number if, for all , there exists a natural number such that for all we have If is a sequence of complex numbers rather than a sequence of real numbers, this last formula can still be used to define convergence, with the provision that denotes the complex modulus, i.e. . If is a sequence of points in a metric space, then the formula can be used to define convergence, if the expression is replaced by the