Paper 4, Section I, E

Numbers and Sets | Part IA, 2013

Let (xn)n=1\left(x_{n}\right)_{n=1}^{\infty} be a sequence of real numbers. What does it mean to say that the sequence (xn)\left(x_{n}\right) is convergent? What does it mean to say the series xn\sum x_{n} is convergent? Show that if xn\sum x_{n} is convergent, then the sequence (xn)\left(x_{n}\right) converges to zero. Show that the converse is not necessarily true.

Typos? Please submit corrections to this page on GitHub.