Convergence of series

Real Analysis
Post Reply
User avatar
Tolaso J Kos
Administrator
Administrator
Posts: 867
Joined: Sat Nov 07, 2015 6:12 pm
Location: Larisa
Contact:

Convergence of series

#1

Post by Tolaso J Kos »

Let \( a_n =\underbrace{\sin \left ( \sin \left ( \sin \cdots (\sin x) \cdots \right ) \right )}_{n \; \rm {times}} \) and \( x \in (0, \pi/2) \). Examine if the series:

$$ S=\sum_{n=1}^{\infty} a_n $$

converges.

Do the same question for the series: \( \displaystyle S=\sum_{n=1}^{\infty}a_n^r , \;\; r\in \mathbb{R}^+ \).
Imagination is much more important than knowledge.
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 17 guests