Absense of limit is not always an infinity, e.g. for sequence (-1)^n. Even if sequence is unbounded, it does not always converge to infinity, e.g. n^((1+(-1)^n

Absense of limit is not always an infinity, e.g. for sequence (-1)^n. Even if sequence is unbounded, it does not always converge to infinity, e.g. n^((1+(-1)^n)/2): 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 1, 16, 1, 18, 1, 20 ... Convergence of sequence x(n) to infinity by definition is: for each real number ε>0 there exists a natural number N(ε) such that for every number n≥N(ε) we have |x(n)|>ε.