6. Let sum _(n=1)a_(n) and sum _(n=1)b_(n) be series of non-negative terms and suppose that a_(1)leqslant b_(1),a_(2)leqslant b_(2),a_(3)leqslant b_(3),ldots ,a_(n)leqslant b_(n),ldots sum _(n=1)a_(n)leqslant sum _(n=1)b_(n) and sum _(n=1)b_(n) diverges, what can be said about the convergence of sum _(n=1)a_(n) by the comparison test? ii sum _(n=1)a_(n)leqslant sum _(n=1)b_(n) and sum _(n=1)a_(n) what can be said about the convergence of sum _(n=1)b_(n) by the comparison test?

i) Since is a series of non-negative terms and diverges, we can conclude that also diverges by the comparison test.ii) Since converges and , we can conclude that also converges by the comparison test.