Practice Homework 6 -- Summation and Solving Recurrence Relations

1. Convert each of the following sums to summation notation:
   1. 2 + 4 + 6 + ... + 20
      

   2. 2 + 5 + 8 + ... + 23
      

   3. 1/1 + 1/2 + 1/3 + ... + 1/10
      

2. Use the summation formulas given on the web page to solve each of the following:
   1. 1 + 2 + 3 + 4 + ... + 14

      1 + 2 + ... + 14 = 14(15)/2 = 105
      

   2. 1 + 2 + 4 + 8 + ... + 128

      1 + 2 + ... + 128 = 20 + 21 + ... + 27 = 28 - 1 = 255
      

   3. 1 + 4 + 9 + 16 + ... + 64

      1 + 4 + ... + 64 = (8)(9)(17)/6 = 204
      

   4. 1 + 8 + 27 + 64 + ... + 512

      1 + 8 + ... + 512 = (82)(92)/4 = 1,296
      

   5. 1 + 3 + 9 + 27 + ... + 6,561

      1 + 3 + ... + 6,561 = (39 - 1)/2 = 9,841
      

   6. 1 + 4 + 18 + 96 + ... + 35,280
      

      1 + 4 + ... + 35,280 = 8! - 1 = 40,319