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数列是函数概念的继续和延伸,数列试题不仅注重考查同学们的运算能力、分析问题和解决问题的能力,更重视对同学们理性思维和创新意识的考查。而创新题正是考查同学们对数列问题的“观察、猜测、抽象、概括、计算、证明、延伸”的绝好载体。这类题型以数列、不等式、函数、直线与曲线为载体,主要考查同学们观察发现,类比转化以及运用数学知识分析和解决问题的能力。下面举例谈谈数列创新题的基本类型及求解策略。
The sequence of numbers is the continuation and extension of the concept of function. The series of questions not only pays attention to examining the students ’computing abilities, analyzing problems and solving problems, but also pays more attention to the students’ rational thinking and innovative consciousness examination. The problem of innovation is the perfect carrier for examining students’ observation, speculation, abstraction, generalization, calculation, proof and extension of sequence problems. This type of questions with the sequence, inequality, function, straight line and curve as the carrier, the main test students observe the discovery, analogy conversion and the use of mathematical knowledge to analyze and solve problems. The following examples talk about the basic types of numerical innovation and solving strategies.