Calculus: Derivatives: General Problems – #27837

Question: Give an example of 2 sequences \(\left\{ {{a}_{n}} \right\}\) and \(\left\{ {{b}_{n}} \right\}\) such that;

a – \(\left\{ {{a}_{n}} \right\}\) and \(\left\{ {{b}_{n}} \right\}\) are divergent, but \(\left\{ {{a}_{n}}+{{b}_{n}} \right\}\) is convergent

b- \(\left\{ {{a}_{n}} \right\}\) is convergent, \(\left\{ {{b}_{n}} \right\}\) is divergent, and \(\left\{ {{a}_{n}}{{b}_{n}} \right\}\) is divergent

c- \(\left\{ {{a}_{n}} \right\}\) is divergent, and \(\left\{ \left| {{a}_{n}} \right| \right\}\) is convergent

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