show that the sequence optional let an be a monotone decreasing zero s
Search for question
Question
OPTIONAL Let (an) be a monotone decreasing zero sequence. Show that the sequence b_{n}:=a_{1}-a_{2}+a_{3}-a_{4} \pm \cdots \pm a_{n}=\sum_{k=1}^{n}(-1)^{n+1} a_{n} is convergent.