2) correct, 2 | UvVN | ≤ UN 2+VN 2-> 0

3) Error, the counterexample un=vn= 1/n, but σ1/n 2 converges.

4) Correct, as long as cn converges.

5) Correct, as long as an diverges.

6) The error should be conditional convergence.

Prove by the standard of prudence

Magnification | ((v (n+1)+u (n+1)) ...+((v (n+p)+u (n+p)) |, greater than.

|||| u (n+ 1)+ ...+u (n+p) || v (n+1)+...+v (n+p) ||, while | u (n+1)+. N' is less than any number a/2, so take N''=max{N, N'}, when n >; When n' || u (n+1)+...+u (n+p) |-v (n+1)+...+v (n+p) | > a/2, the certificate is completed.

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