If you can show that all subsequences of a Cauchy sequence are convergent then you can use: Every convergent sequence (with limit s, say) is a Cauchy sequence, since, given any real number ε > 0, beyond some fixed point, every term of sequence is within distance ε/2 of s, so any two terms of the sequence are within distance ε of each other.
Hope this helps. There may be something here: MATH 138BH that will help you. Good luck.
John
My calculator said it, I believe it, that settles it
