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1问题呈现题目:设S_n数列{a_n}的前n项和,S_n=(-1)~na_n-1/2~n,n∈N_+,则(1)a_3=____;(2)S_1+S_2+S_3+…+S_(100)=____。背景说明:这道题出现在一次常规练习中,解答结果显示第(1)问正确率还比较高,但第(2)问全班60名学生竟有45人答不出来或出现错误。笔者就第(2)问的学生答题情况进行了统计,主要有4种情况:(1)试了几个,结果不太明显,故而放弃(10人);(2)时间有点紧,加之该题的位置偏后,放弃了(15人);(3)运算过程中把n为奇数、偶数的结果弄反了,导致出错(11人);(4)知道要对n分奇偶数讨论,但在转化过程中,绕弯多了,没有结
(1) a_3 = ____; (2) S_1 + 1, n_n + 1, n_n + 1, S_2 + S_3 + ... + S_ (100) = ____. Background description: This question appears in a regular exercise. The answer shows that the correct answer is still high at (1), but (2) as many as 45 of the 60 students in the entire school can not answer or make an error. The author of (2) asked the students to answer the situation statistics, there are four main situations: (1) a few trials, the result is not obvious, so give up (10); (2) a bit tight time, coupled with the (15); (3) the operation of the odd number of n, even the result of the inverse, resulting in an error (11); (4) However, in the conversion process, winding more, no knot