1049 11.1 Sequences and Series Use a graphing calculator to evaluate each series. See Example 4. 55. a10 i=1 14i2 - 52 56. a10 i=1 1i3 - 62 57. a 9 j=3 13j - j22 58. a10 k=5 1k2 - 4k + 72 Write the terms for each series and evaluate the sum, given that x1 = -2, x2 = -1, x3 = 0, x4 = 1, and x5 = 2. See Examples 5(a) and 5(b). 59. a 5 i=1 xi 60. a 5 i=1 -xi 61. a 5 i=1 12xi + 32 62. a 4 i=1 1-3xi - 22 63. a 3 i=1 13xi - xi 22 64. a 3 i=1 1xi 2 + x i2 65. a 5 i=2 xi + 1 xi + 2 66. a 5 i=1 xi xi + 3 67. a 4 i=1 xi 3 + 1000 xi + 10 68. a 4 i=1 xi 3 - 64 xi - 4 Write the terms of a 4 i=1 ƒ1xi2Δx, with x1 = 0, x2 = 2, x3 = 4, x4 = 6, and Δx = 0.5, for each function. Evaluate the sum. See Example 5(c). 69. ƒ1x2 = 4x - 7 70. ƒ1x2 = 6 + 2x 71. ƒ1x2 = 2x2 72. ƒ1x2 = x2 - 1 73. ƒ1x2 = -2 x + 1 74. ƒ1x2 = 5 2x - 1 Use the summation properties and rules to evaluate each series. See Examples 6 and 7. 75. a100 i=1 6 76. a20 i=1 5 77. a15 i=1 i2 78. a50 i=1 2i3 79. a 5 i=1 15i + 32 80. a 5 i=1 18i - 12 81. a 5 i=1 14i2 - 2i + 62 82. a 6 i=1 12 + i - i22 83. a 4 i=1 13i3 + 2i - 42 84. a 6 i=1 1i2 + 2i32 Concept Check Use summation notation to write each series.* 85. 1 3112 + 1 3122 + 1 3132 + g+ 1 3192 86. 5 1 + 1 + 5 1 + 2 + 5 1 + 3 + g+ 5 1 + 15 87. 1 - 1 2 + 1 4 - 1 8 + g1 128 88. 1 - 1 4 + 1 9 - 1 16 + g1 400 Use the sequence feature of a graphing calculator to graph the first ten terms of each sequence as defined. Use the graph to make a conjecture as to whether the sequence converges or diverges. If it converges, determine the number to which it converges. 89. an = n + 4 2n 90. an = 1 + 4n 2n 91. an = 2en 92. an = n1n + 22 93. an = a1 + 1 nb n 94. an = 11 + n21/n * These exercises were suggested by Joe Lloyd Harris, Gulf Coast Community College.
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