EDB — 0F0

Exercises

1. [0F0]Note:Exam of 9th APr 2011.Let \((a_ n)\) be a sequence of real numbers (not necessarily positive) such that the series \(∑_{n=1}^∞ a_ n\) converges to \(a∈{\mathbb {R}}\); let \(b_ n=\frac{a_ 1+\cdots +a_ n}{n}\); show that if the series \(∑_{n=1}^∞ b_ n\) converges then \(a=0\).