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数列求和一直是高考的热点内容.通过研究近几年的高考试卷我们可以发现,通项形如“dn=an bn+cn(其中bn为周期数列)”的数列{dn}的求和问题正悄然升温.我们暂且称数列{dn}为“类周期数列”.一、并项与迭代求和策略在“类周期数列”{dn}中,设数列{bn}的周期为T(T∈*N),数列{dn}的前n项和为Sn.将数列{dn}从第一项起,依次每连续的T项“捆绑”合并成一项,构造一个新数列{pk}(其中pk=dTk-(T-1)+dTk-(T-2)+…+dTk-1+dTk,k∈*N),并求其通项公式.当数列{dn}的项数n为T的倍数(即n=Tm,m∈*N)时,
Summation of the series has always been a hot topic in college entrance examination. Through the study of the college entrance examination papers in recent years, we can find that general terms such as “dn = an bn + cn (where bn is the periodic sequence) ” And the problem is quietly warming up. Let us now say that the number of columns {dn} for the “class cycle number.” A, and items and iterative sum strategy in the “class cycle series ” {dn}, the number of columns {bn} The period is T (T ∈ * N), the first n terms of the sequence {dn} are Sn, and the sequence {dn} is merged into one item from the first term, followed by each successive T term The new sequence {pk} (where pk = dTk- (T-1) + dTk- (T-2) + ... + dTk- 1 + dTk, k∈ * N) } Is n, which is a multiple of T (ie, n = Tm, m∈ * N)