题目

若无穷数列满足：，且对任意，(s，k，l，)都有，则称数列为“T”数列.（1）证明：正项无穷等差数列是“T”数列；（2）记正项等比数列的前n项之和为，若数列是“T”数列，求数列公比的取值范围；（3）若数列是“T”数列，且数列的前n项之和满足，求证：数列是等差数列. 答案：【答案】（1）答案见解析.（2）.（3）答案见解析【解析】（1），根据题意得到，得到证明.（2）讨论，，三种情况，时，计算，时，计算，得到答案.（3）计算得到，根据题意得到，利用退项相减得到，得到证明.（1），因为正项无穷等差数列，所以，且，所以，所以正项无穷等差数列是“T”数列.（2请认真阅读下列短文，从短文后各题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。I put my sunglasses on and took a deep breath. We began to walk down the street on her first day of school with her hand held tightly in mine. I knew she would be crying in a few minutes, because she always did that when she was ______ about a new environment.On the way to school, I told her repeatedly how ______ her new school life would be and expected she would feel ______. But when she saw the massive group of students everywhere, her face at once fell and the tears (眼泪) came into her eyes. “You can do this, sweetie. Everyone has a place in line; let’s go to find yours.”We lined up to enter the school. Just as she was about to hold on to my leg, her friend from preschool stood next to her. Suddenly, she became ______ and reached out for her friend’s hand. And as the teacher began to ______ them all into the school, she wasn’t crying, but smiling.Honestly, I was ______ to say goodbye when I saw those little feet walk into that big building. I hid the tears behind my sunglasses and waved my hand as she walked inside.All day I ______ what she was doing. As I waited to pick her up, I felt like a child standing in line to ______ Santa. She came out with her hand waving and her arms outstretched (伸展). “I didn’t cry again, Mommy,” she said, ______ hugging (拥抱)me and showing me her backpack full of goodies.During two hours of listening to the details of her day, we laughed and talked about all the _____she had. And just like her, I didn’t cry again either, I knew my daughter has grown up.【1】A. crazy B. careful C. curious D. nervous【2】A. amazing B. comfortable C. valuable D. important【3】A. safe B. relaxed C. lucky D. proud【4】A. confident B. silent C. active D. serious【5】A. walk B. send C. drive D. push【6】A. brave B. unwilling C. happy D. natural【7】A. followed B. asked C. watched D. wondered【8】A. calm B. feel C. meet D. thank【9】A. shyly B. excitedly C. politely D. suddenly【10】A. experiences B. classes C. students D. teachers