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迭代法也称辗转法,在计算机编程和高等数学中有着广泛的应用.实际上,迭代法在解决高中有关递推数列问题时也非常的有用,是化归思想的一种体现.特别是在新课标将数学归纳法纳入理科选修内容后,迭代思想的重要性更加突出.下面就以几例来说明.一、形如an+1=pan+q型例1(2014年新课标全国Ⅱ改编)已知数列{an}满足a1=1,an+1=3an+1.求{an}的通项公式.
Iteration method, also called tumbling method, has a wide range of applications in computer programming and advanced mathematics.In fact, the iterative method is also very useful in solving high school recursion sequence problems, which is a manifestation of the thought of returning to the past The new curriculum will be the mathematical induction into the science elective content, the importance of iterative thinking is even more prominent. Here are a few examples to illustrate. First, the form as an + 1 = pan + q Example 1 (2014 New Curriculum National Ⅱ adapted) known sequence {an} satisfy a1 = 1, an + 1 = 3an + 1. Find {an} general formula.