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在数学教学中培养学生的观察能力,是学生学好数学的关键之一,也是培养其他思维能力的基础。下面浅谈一下在这方面的做法与体会。一、引导学生观察条件中的数字或字母的变化规律及位置特点例1 已知数列{a_n}的前五项是1,2,4,7,11,试写出这个数列的一个通项公式。解:细心观察后知:相邻两项中后项与前项的差有规律: a_z-c_1=2-1=1, a_3-a_2=4-2=2, a_4-a_3=7-4=3, a_5-a_6=11-7=4, 由此可得 a_n-a_n-1=n-1再把上面(n-1)个式子相加得左边=a_n-a_1;右边=1+2+3+……+(n-1)=(n-1)/2
Training student’s observation ability in mathematics teaching is one of the keys for students to learn mathematics well, and it is also the basis for training other thinking ability. Let’s talk about the practices and experiences in this area. First, guide students to observe the condition of the number or letter of the law of change and location characteristics Example 1 Known series {a_n} of the first five is 1,2,4,7,11, try to write a general formula for this series . Solution: After careful observation, there is a regularity between the difference between the two items in the adjacent two items: a_z-c_1=2-1=1, a_3-a_2=4-2=2, a_4-a_3=7-4= 3, a_5-a_6=11-7=4, from which we can get a_n-a_n-1=n-1 and add the above (n-1) formulas to the left = a_n-a_1; right = 1+2 +3+......+(n-1)=(n-1)/2