Question

若级数∑Un收敛于S,级数∑【un+un+1】则收敛于

{n从1到无穷｝

Answer 1

∑【un+un+1】收敛于2s-u1

追问

怎么做的呢？解释下理由好吗？谢谢

追答

∑【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