Math 381                                                                Name: KEY
Quiz 5




  1. For each of the sequences MATH below determine MATH and MATH
    1. MATH

      2. MATH
       
    2. MATH

      3. MATH
  2. Let $s_{1}=2$ and MATH
    1. Use mathematical induction to show that $0<s_{n}\leq2$ for all $n\in\QTR{Bbb}{N}.$

      2. MATH
       
    2. Show that MATH is a nonincreasing sequence.

      3. MATH
       
    3. Explain why $\lim s_{n}$ exists and find $\lim s_{n}.$

      4. MATH

      MATH

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