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Convergence Tests

Hello.

Does anyone know about convergence tests and if so could they check if my solutions are correct.

I can upload the questions and my solutions to them later.

Just made an acc here

Thanks

N
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by L'Evil Wolf
Hello.

Does anyone know about convergence tests and if so could they check if my solutions are correct.

I can upload the questions and my solutions to them later.

Just made an acc here

Thanks

N


I am sure somebody will
Reply 2
Avatar for L'Evil Wolf
L'Evil Wolf
OP
6
Original post by TeeEm
I am sure somebody will


thnx for the reply
Reply 3
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L'Evil Wolf
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pls can someone view the link:

my work is on there thnx

http://imgur.com/a/IHjiO

N
Original post by L'Evil Wolf
pls can someone view the link:

my work is on there thnx

http://imgur.com/a/IHjiO

N


This is right. The last "series" should be "sequence" though.
(edited 8 years ago)
Reply 5
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L'Evil Wolf
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Original post by morgan8002
This is right. The last "series" should be "sequence" though.


ah thank you, apart from that though is everything fine. When I checked whether my answer was correct on wolfram they said something about a root test idk.
Original post by L'Evil Wolf
ah thank you, apart from that though is everything fine. When I checked whether my answer was correct on wolfram they said something about a root test idk.


There's many ways to do it. Yours is probably the simplest. Root test is covered later and is more complicated.
Reply 7
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L'Evil Wolf
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Original post by morgan8002
There's many ways to do it. Yours is probably the simplest. Root test is covered later and is more complicated.


Thank you morgan,

Wolfram says that it is a series though - are you sure it is a sequence. I am not sure myself.

Thanks for the help btw
Original post by L'Evil Wolf
Thank you morgan,

Wolfram says that it is a series though - are you sure it is a sequence. I am not sure myself.

Thanks for the help btw


It depends on what you are referring to. Let mx=x+11+2xm_x = \dfrac{x+1}{1+2x}. Then (mx)x∈N\big(m_x\big)_{x\in \mathbb{N}} is a sequence, but ∑x=0∞mx\displaystyle\sum_{x=0}^{\infty} m_x is a series.
In this case the sequence converges to 0.5 but the series does not converge.

The series is defined as the limit of the sequence of partial sums, lim⁡n→∞∑x=0nmx\displaystyle\lim_{n\rightarrow \infty}\displaystyle\sum_{x=0}^{n} m_x. This could be what Wolfram is referring to as sequence.

Remember that a sequence is defined as a function from a subset of Z\mathbb{Z}(often N\mathbb{N}). A series is just a number if it converges.
Reply 9
Avatar for L'Evil Wolf
L'Evil Wolf
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6
Original post by morgan8002
It depends on what you are referring to. Let mx=x+11+2xm_x = \dfrac{x+1}{1+2x}. Then (mx)x∈N\big(m_x\big)_{x\in \mathbb{N}} is a sequence, but ∑x=0∞mx\displaystyle\sum_{x=0}^{\infty} m_x is a series.
In this case the sequence converges to 0.5 but the series does not converge.

The series is defined as the limit of the sequence of partial sums, lim⁡n→∞∑x=0nmx\displaystyle\lim_{n\rightarrow \infty}\displaystyle\sum_{x=0}^{n} m_x. This could be what Wolfram is referring to as sequence.

Remember that a sequence is defined as a function from a subset of Z\mathbb{Z}(often N\mathbb{N}). A series is just a number if it converges.


Thank you morgan.

Yes series is what I am most nearly referring to.

Eng not first language srry.

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