1. The problem statement, all variables and given/known data Using only the definition of a limit of a sequence prove that lim n->infinity tanh(n)=1 2. Relevant equations 3. The attempt at a solution My attempt at the solution is as follows. If 1 is the limit of the sequence then for every [tex]\epsilon[/tex]>0, there exists an number such that n>N for every n, such that we have |tanh(n)-1|<[tex]\epsilon[/tex] apply the appropriate hyperbolic identity I re-write this as. |e^2n-1/(e^2n+1) -1 |< [tex]\epsilon[/tex] as tanh(n)< 1 for every sufficiently large n we have 1-(e^2n-1/(e^2n+1)) < [tex]\epsilon[/tex] After this im stumped, our textbook is very poor so are the notes. Any help is welcome thanks in advanced.