Or something like that (I cannot think exactly what it is now).

How about and .1.) if (an) and (bn) are divergent, then also (an + bn) and (an - bn) are divergent. I believe this is false.

Since this converges it must mean that coverges.2.) (an)^2 converges if and only if (abs(an)) converges. true?

Look at first post.3.) if (an) and (bn) are convergent, then also max(an, bn) is convergent. true?

No consider the sequence of partial harmonic sums.4.) if (an+1 - an) converges to zero, then (an) converges. *the n+1 is all a subscript*

Yes. And furthermore it converges to zero. This is the ratio test.5.) if an > 0 and ((an+1)/(an)) < 1 for all n, then (an) converges. *again the n+1 is all a subscript*

I just want to know if they're true or false.