Absolute convergence criterion

Real Analysis
Post Reply
Tsakanikas Nickos
Community Team
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

Absolute convergence criterion

#1

Post by Tsakanikas Nickos »

Let \( \displaystyle \left( y_{n} \right)_{n\in \mathbb{N}} \) be a sequence of real numbers such that : for all sequences \( \displaystyle \left( x_{n} \right)_{n\in \mathbb{N}} \) of real numbers with \( \displaystyle \lim_{n}x_{n} = 0 \) the series \( \displaystyle \sum_{n=1}^{\infty} x_{n}y_{n} \) converges. Then \( \displaystyle \sum_{n=1}^{\infty} | y_{n} | < + \infty \).
admin
Administrator
Administrator
Posts: 40
Joined: Mon Oct 26, 2015 12:27 pm

Re: Absolute convergence criterion

#2

Post by admin »

A solution may be found here.
admin
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 9 guests