题目

IV．阅读理解（每题2分，满分40分） A university graduate described as a “respectable and intelligent” woman is seeking professional help after being convicted of (证明有…罪) shoplifting for the second time in six months . Aha Luz , recently studying for PhD has been told she could end up behind bars unless she can control the desire to steal from shops. Luz , who lives with her partner in Fitzwilliam Road , Cambridge , admitted stealing clothes worth 9.95 pounds from John Lewis in Oxford Street , London , on March 9. Phillip Lomoyne , prosecuting (起诉), said Luz selec3．（1）$\frac{1}{a-b}$+$\frac{1}{a+b}$+$\frac{2a}{{a}^{2}+{b}^{2}}$+$\frac{4{a}^{3}}{{a}^{4}+{b}^{4}}$；（2）$\frac{1}{x（x+1）}$+$\frac{1}{（x+1）（x+2）}$+$\frac{1}{（x+2）（x+3）}$+…+$\frac{1}{（x+99）（x+100）}$（3）$\frac{1}{1+a}$+$\frac{1}{1-a}$+$\frac{1}{（1+a）（1+2a）}$+$\frac{1}{（1-a）（1-2a）}$．