Is (2n+3)/(4n+5) a Convergent Series?

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SUMMARY

The expression (2n+3)/(4n+5) represents a sequence that converges to 1/2, but it does not form a convergent series. According to the established theory, for a series ∑{an} to be convergent, the limit of the sequence {an} must approach 0. In this case, the limit of {an} is 1/2, indicating that the series ∑_{n=0}^∞ (2n+3)/(4n+5) diverges. This distinction between sequences and series is crucial in understanding convergence in mathematical analysis.

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Homework Statement


Theory:
{an} is Convegent series then lim {an}=0
O.K. But let {an}=(2n+3)/(4n+5) is Convegent series and lim an=1/2


Homework Equations


Elucidation for this look wanted



The Attempt at a Solution

 
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Hi m_s_a! :smile:

I think they mean if ∑{an} is Convegent series then lim {an}=0. :smile:
 
tiny-tim said:
Hi m_s_a! :smile:

I think they mean if ∑{an} is Convegent series then lim {an}=0. :smile:

Hi _>inf :biggrin:
:-pLast answer waits
please wait whith me :smile:
What saw you in how the English learns correctly and in extremely short period
 
m_s_a said:
Hi _>inf :biggrin:
:-pLast answer waits
please wait whith me :smile:
What saw you in how the English learns correctly and in extremely short period

Hi \aleph_{\aleph_0} ! :biggrin: :biggrin:

Reading your words is always a pleasure! :approve:

Even though I have no idea what you mean! :smile:

What language are you translating from? :smile:
 
Tell me what is a state that hates people who belong to it? :wink:
 
tiny-tim said:
What language are you translating from? :smile:

Japanese to English translations sounds so much like this. But, I would also love to know.

O.K. But let {an}=(2n+3)/(4n+5) is Convegent series and lim an=1/2

{an}=(2n+3)/(4n+5) is not convergent if you saying it is or someone said that.
 
m_s_a said:

Homework Statement


Theory:
{an} is Convegent series then lim {an}=0
O.K. But let {an}=(2n+3)/(4n+5) is Convegent series and lim an=1/2
"Series" (in mathematics, not general English) means specifically a "sum" while "sequence" does not. (2n+3)/(4n+5) is a sequence that converges to 1/2. The series
\Sum_{n=0}^\infty \frac{2n+3}{4n+5}
does NOT converge.

Tell me what is a state that hates people who belong to it?
From recent events I am tempted to say Myanmar.
 
rootX said:
Japanese to English translations sounds so much like this. But, I would also love to know.



{an}=(2n+3)/(4n+5) is not convergent if you saying it is or someone said that.

We know love
Ten years ago you appreciate and respected by States
The exchange of the same feeling
Because the person do something ?
Changed the image of an entire people
Why? Why?
We hate that person like you.
Believe me
How We See previous How?
I said: ball or hatred
Because we are not enemies of anyone
But now everyone Why do they hate us?
We wronged wronged wronged.
 
HallsofIvy said:
"Series" (in mathematics, not general English) means specifically a "sum" while "sequence" does not. (2n+3)/(4n+5) is a sequence that converges to 1/2. The series
\Sum_{n=0}^\infty \frac{2n+3}{4n+5}
does NOT converge.


From recent events I am tempted to say Myanmar.

Is circulated to all people
Contrary to our nation
Can not enter the country before the recent events
Do not agree with the work done by
Not us
 
  • #10
Sorry :smile:
 

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