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Unformatted text preview: N proof that lim n 1 n +1 = 0. * Note: This is book problem 2b. 2. Using only the AP give a direct N verication that b 2 n + 1 n + 3 B converges. ** Note: This is book problem 3a. 3. For the sequence { a n } dened in book Example 2.3 show that x Q (0 , 1] there are innitely ** many indices n such that a n = x . Clariy what this is saying with a specic example. Note: This is book problem 5 plus a bit more. 4. Suppose that { a n } converges to a > 0. Show N st n N a n > 0. * Note: This is book problem 6. 5. Dene a 1 = 1 and a n +1 = a n + 1 n if a 2 n 2 a n 1 n if a 2 n > 2 (a) Write the rst ve terms of this sequence. * (b) Show that n ,  a n 2  < 2 n . ** (c) Use this property to show the sequence converges to 2. * Note: This is book problem 12 broken up plus a bit more....
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Math

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