I've been thinking in circles over this problem so I thought I'd give this forum a try - I hope someone can help.

I've been given a definition:

For all epsilon>0 , there exists a natural number N such that if |Xn-L| < epsilon, then n is greater than or equal to N.

I need to either find an infinite sequence Xn which converges but does not satisfy the conditon above OR

find a sequence Xn and L which do satisfy the condition above but Xn does not converge to L.

I'd be grateful if anybody could talk me through what features such a sequence should have.

Thanks