- #1
m_s_a
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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
tiny-tim said:Hi m_s_a!
I think they mean if ∑{an} is Convegent series then lim {an}=0.
m_s_a said:Hi _>inf
:tongue:Last answer waits
please wait whith me :rofl:
What saw you in how the English learns correctly and in extremely short period
tiny-tim said:What language are you translating from?
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 seriesm_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
From recent events I am tempted to say Myanmar.Tell me what is a state that hates people who belong to it?
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.
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
[tex]\Sum_{n=0}^\infty \frac{2n+3}{4n+5}[/tex]
does NOT converge.
From recent events I am tempted to say Myanmar.
The equation for convergence of (2n+3)/(4n+5) is lim(n→∞) (2n+3)/(4n+5).
The value of the limit represents the value towards which the sequence approaches as n becomes increasingly large.
To determine if the sequence converges, you can evaluate the limit of the sequence as n approaches infinity. If the limit is a finite number, then the sequence converges. If the limit is infinity or negative infinity, then the sequence diverges.
The method for finding the limit of a sequence is to simplify the equation and then substitute ∞ for n. If the resulting expression is indeterminate (e.g. 0/0 or ∞/∞), you can use techniques such as L'Hôpital's rule or the squeeze theorem to evaluate the limit.
The convergence of a sequence is significant because it tells us whether the terms in the sequence will eventually become closer and closer to a specific value or if they will continue to fluctuate indefinitely. This information is important in many mathematical and scientific applications.