Unformatted text preview: where . Prove that . 2. Show that 3. Prove the Monotone Convergence Theorem. 4. Prove for some constant , then . 5. Suppose . Consider the sequence . Does this sequence converge? Does the sequence diverge? Will it converge for some values of a and b but not for others? 6. Prove the sequence defined by and for all n converges. 7. Use the Nested Interval Theorem to prove the Bolzano-Weierstrass Theorem 8. Prove that is a sequence converges to some limit L , then each of its subsequences also converges to L ....
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- Spring '08