Your definition of convergence is not correct. It should be

There existsL in Real numberssuch that forall E>0 such that there exists N in Natural numberssuch thatn>/= N implies |xn-L|<E.

The negation of the definition of convergence should be: For every real number there exists a real number such that for every natural number there is a natural number such that Use this to prove the divergence of where Hint: Given let if and if