The discussion revolves around determining whether the sequence defined by {4 + sin(1/2 * pi * n)} converges or diverges, and if it converges, identifying the limit. Participants express confusion regarding the oscillatory nature of the sine function and its implications for the limit of the sequence.
The discussion is active, with various interpretations being explored regarding the limit of the sequence. Some participants have offered insights into the nature of the sequence and its possible values, while others are questioning the fundamental definitions of limits and the properties required for convergence.
Participants note that the sequence oscillates between three specific values: 3, 4, and 5, leading to questions about the existence of a single limit. There is also mention of the need to understand the definition of a limit in the context of this sequence.
Sarah Kenney said:Homework Statement
I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit.
{4+sin(1/2*pi*n)}
The Attempt at a Solution
This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that would go back and forth. So does that mean that the limit does not exist?
Thanks in advance.
PeroK said:If the limit does exist, what could it be?
Sarah Kenney said:Would the limit be 5 since sin(pi\2) is 1?
Sarah Kenney said:Oh, so because it oscillates between -1 and 1, then the limit is from 3 to 5?
Sarah Kenney said:Homework Statement
I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit.
{4+sin(1/2*pi*n)}
The Attempt at a Solution
This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that would go back and forth. So does that mean that the limit does not exist?
Thanks in advance.