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Originally Posted by

**marcopolon2** 1. Every unbounded sequence is divergent.

If a sequence is convergent then it is bounded. Now take the contrapositive statement.

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2. Every convergent sequence is bounded.

Just answered above.

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3. A decreasing sequence is convergent if and only if it is bounded above.

Take $\displaystyle a_n = -n$.

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5. If a function is continuous on the interval I, then it is integrable over I.

Yes.

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6. Differentiability is the sufficient but not necessary condition for integrability.

Yes.