1. The problem statement, all variables and given/known data Courant states that a convergent sequence is necessarily bounded; that is, for all n, the absolute value of term an is less than or equal to some number M. My question is does this apply to the sequence given by an = 1/(n-1)? 2. Relevant equations As n approaches infinity, an approaches zero, so the sequence converges. 3. The attempt at a solution At n = 1, 1/(n-1) is larger than any number M, which suggests the sequence is not bounded. Should we only consider terms for n > 1, in which case the sequence would be bounded by 1 and still converge to 0?