材料一：小琳性格内向，在小学里不善于与老师、同学交往，学习成绩也不尽如人意。升入初中后，小琳所在的班级团结友爱，老师经常鼓励她，班里的同学都主动和她交朋友，她的性格变得开朗起来。生本课堂上，同学们大方自信的展示深深触动了她，小琳暗下决心努力学习，她认真预习、上课专心倾听、积极参与小组合作，她的展示从一开始的声音小、不敢抬头看同学慢慢变得大方自信起来，学习成绩也有了很大的进步。这个学期，学校组织“达人秀”活动，小琳报名参加了，在初赛中她的古筝演奏获得了音乐老师的认可，因此入围决赛，她每天勤奋练习，争取在决赛中表现出色。

材料二：2016年度“全国十佳最美孝心少年”向小康，就读于湘西古丈县第二完全小学，是古丈县青少年校外活动中心合唱团领唱队员。这个眼睛会说话、歌声很动听的苗族小女孩，被网友称为“又一个未来的宋祖英”。生活当中的向小康乖巧懂事，善良孝顺。她的妈妈身体不太好，父亲靠打零工维持家里生计。小康不但要帮助爸爸照顾病情日益加重的妈妈，还要承担家中一切大小事务。向小康并没有因为照顾家庭和妈妈而耽误学习，她深知学习机会来之不易，上课她是最认真听讲的，课后抓住一切可能的时间刻苦学习，成绩优异，一直是班上的学习委员。

（Ⅰ）求证： $\left\{\frac{1}{a_n}+1\right\}$ 是等比数列，并求{a_n}的通项公式a_n；

（Ⅱ）数列{b_n}满足 $b_n=\left(2^n-1\right)\cdot \frac{n}{2^{n-1}}\cdot a_n$ ，数列{b_n}的前n项和为T_n，若不等式 ${\left(-1\right)}^n\lambda <T_n+\frac{n}{2^{n-1}}$ 对一切n∈N^*恒成立，求λ的取值范围．

    Five years ago, when I taught art at a school in Seattle, I used Tinkertoys as a test at the beginning of a term to find out something about my students. I put a small set of Tinkertoys in front of each student, and said: “Make something out of the Tinkertoys. You have 45 minutes today - and 45minutes each day for the rest of the week.”

    A few students hesitated to start. They waited to see the rest of the class would do. Several others checked the instructions and made something according to one of the model plans provided. Another group built something out of their own imaginations.

    Once I had a boy who worked experimentally with Tinkertoys in his free time. His constructions filled a shelf in the art classroom and a good part of his bedroom at home. I was delighted at the presence of such a student. Here was an exceptionally creative mind at work. His presence meant that I had an unexpected teaching assistant in class whose creativity would infect（感染）other students.

    Encouraging this kind of thinking has a downside. I ran the risk of losing those students who had a different style of thinking. Without fail one would declare, “But I'm just not creative.”

    “Do you dream at night when you're asleep?”

    “Oh, sure.”

    “So tell me one of your most interesting dreams.” The student would tell something wildly imaginative. Flying in the sky or in a time machine or growing three heads. “That's pretty creative. Who does that for you? “

    “Nobody. I do it.”

    “Really-at night, when you're asleep?”

    “Sure.”

    “Try doing it in the daytime, in class, okay?”