# 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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