Real Analysis/Section 2 Exercises/Hints

No Hint. No Hint. No Hint. Use Newton's method to approximate the zeros of the function x2 − c. No Hint. No Hint. No Hint. No Hint. No Hint. No Hint. To show that the sequence converges show that the sequence is bounded and contains two monotone subsequences, each of which converge by the monotone convergence theorem, and whose difference converges to 0. To find the limit, take limits of both sides of the recursion relation to find an equation the limit must satisfy. No Hint. Look carefully at how we defined a telescoping sum. Try to relate this back to the usual comparison test.