若级数∑Un收敛于S,级数∑【un+un+1】则收敛于

问题描述:

若级数∑Un收敛于S,级数∑【un+un+1】则收敛于
{n从1到无穷}

∑【un+un+1】收敛于2s-u1怎么做的呢?解释下理由好吗?谢谢∑【un+un+1】 =∑(n从1到∞)un+∑(n从1到∞)un+1 =s+∑(n从1到∞)un+1 (后面相当于从u2开始相加,所以可化为∑(n从1到∞)un-u1) =s+∑(n从1到∞)un-u1 =s+s-u1 =2s-u1