級數(shù)與冪級數(shù)及其應(yīng)用習(xí)題

1、第十章第十章級數(shù)與冪級數(shù)及其應(yīng)用級數(shù)與冪級數(shù)及其應(yīng)用一、填空題：一、填空題：1.級數(shù)=11(1)3nnn?????2.級數(shù)=.1112nn????3.級數(shù)11(1)nnn?????4.級數(shù)18(1)9nnnn?????5.冪級數(shù)的收斂半徑為???13nnnnx6.級數(shù)13()4nn?????7.設(shè)級數(shù)，當(dāng)時，級數(shù)收斂.???11npnp8.級數(shù).???????????)3121()3121()311(12nn9.級數(shù).112nnn???

2、??10.冪級數(shù)的收斂區(qū)間是.1nnxn???11.級數(shù)的和為.1(ln3)2nnn???12.級數(shù)=.11147kkk?????13.如果級數(shù)，在處收斂，則該級數(shù)在處（填“收1(3)nnnax????1.1x??5x?斂”或“發(fā)散”）.（A）當(dāng)時級數(shù)收斂，當(dāng)時級數(shù)發(fā)散（B）當(dāng)時級數(shù)收斂當(dāng)時1?p1?p1?p1?p級數(shù)發(fā)散（C）當(dāng)時級數(shù)收斂當(dāng)時級數(shù)發(fā)散（D）當(dāng)時級數(shù)收斂當(dāng)時級1?p1?p1?p1?p數(shù)發(fā)散8.正項級數(shù)滿足條件（）時必收斂

3、???1nna(A)(B)(C)(D)0lim???nna1lim1????nnnaa1lim1nnnaa????1lim1??????nnnaa9.下列級數(shù)中為條件收斂的是（）（A）（B）（C）（D）1)1(1?????nnnnnnn????1)1(211)1(nnn????nnn1)1(1????10.在下列級數(shù)中那個是收斂的（）ABCDnn211???111????nnnn11???nn311???11.設(shè)級數(shù)收斂則下列級數(shù)收斂的

4、是（）；1nnU???A.B.11()nnUn????2001nnU????C.D.211nnU????21nnU???12.下列級數(shù)條件收斂是（）A.B.11(1)nnn?????112(1)()3nnn?????C.D.121(1)21nnnn??????131nnn????13.以下級數(shù)絕對收斂的是（）（A）（B）（C）（D）10(1)!nnn?????11(1)nnn?????111(1)cosnnn?????1ln1nnn??