题目

已知Sn是数列{an}的前n项和，且an=Sn-1+2（n≥2），a1=2. （1）求数列{an}的通项公式； （2）设bn=,Tn=bn+1+bn+2+…+b2n,是否存在最大的正整数k，使得对于任意的正整数n,有Tn＞恒成立？若存在，求出k的值；若不存在，说明理由. 答案：（1）an=2·2n-1=2n（2）存在最大正整数k=5使Tn＞恒成立 解析:（1）由已知an=Sn-1+2                                             ① 得an+1=Sn+2                                                ② ②-①，得an+1-an=Sn-Sn-1 (n≥2), ∴an+1=2an (n≥2). 又a1=2,∴a2=a1+2=4=2a1, ∴an+1=2aA farmer had a cow. He took very good care of his cow and one day when it was ill, he was very worried. He telephoned the vet.“What's the problem?”the vet asked him when he arrived.“My cow is ill,”the farmer said.“I don't know what's the matter with her. She's lying down and won't stand up. She won't eat, and she's making a strange noise.”The vet looked at the cow. “She's certainly ill,” he said, “and she needs to take some very strong medicine.”He took a bottle out of his box, and put two pills (药片)into his hand. “Give her these,”he said,“the pills should make her better.”“How should I give them to her?”the farmer asked asked. The vet gave him a long tube(管子).“Put this tube in her mouth,”he said,“then put the pills in the tube and blow(吹). That'll make it.”The next day the vet came to the farm again. The farmer was sitting outside his house and looked more worried.“How is your cow?”the vet asked.“No change,”the farmer said, “I'm feeling very strange myself.”“Oh?”the vet said,“Why?”“I did what you said,”the farmer answered.“I put the tube in the cow's mouth and then put two pills down it.”“And?”the vet asked.“The cow blew (blow的过去式)first,”the farmer said.What medicine did the vet give the farmer?A.A bottle of pills.B.A long tube.C.Two pills.D.A small box.