Question

4.3 Devilish Series The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may dr is why these series have produced so dany fallacies and so many paradoxes. Neils Henrik Abel (Norwegian Mathematician; 1802 - 1829) There is no reason that infinite series must have all positive terms. For example, the alter- nating harmonic series is built from the harmonic series but with every other term negative: 12+3 4+5 Shown in Figure42 are the results of adding a small number of terms of this series. For each of the following, sum the indicated number of terms and then graph the partial sums on the graph provided in the appendix: 65. ...the first nine terms. 66. ...the first ten terms. 67. ...the first eleven terms. 68. .. . the first twelve terms. Partial sum NS Number of terms added Figure 4.2: Partial sums of the alternating harmonic series

Answer 1

l 2. 2 1 ㄐㄧㄧ 6 8 3

(68 S 1 - I6 ) 2 049 8