Soru
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?
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Aytunç
Profesyonel · 6 yıl öğretmeniUzman doğrulaması
Cevap
i) Since $\sum_{n=1}a_{n}$ is a series of non-negative terms and $\sum_{n=1}b_{n}$ diverges, we can conclude that $\sum_{n=1}a_{n}$ also diverges by the comparison test.<br /><br />ii) Since $\sum_{n=1}a_{n}$ converges and $\sum_{n=1}a_{n}\leqslant \sum_{n=1}b_{n}$, we can conclude that $\sum_{n=1}b_{n}$ also converges by the comparison test.
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