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the question in this link:

http://img372.imageshack.us/img372/7929/76106583tn6.gif [Broken]

??

http://img372.imageshack.us/img372/7929/76106583tn6.gif [Broken]

??

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- Thread starter transgalactic
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- #1

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the question in this link:

http://img372.imageshack.us/img372/7929/76106583tn6.gif [Broken]

??

http://img372.imageshack.us/img372/7929/76106583tn6.gif [Broken]

??

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- #2

Office_Shredder

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- #3

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its common sense

if a(n) converges to a

then if we take the function who takes the biggest member

of course it will pick the closest to "a"

i dont know how to transform these word into math

??

- #4

Office_Shredder

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So.... if you take n>N, what can you say about |b

- #5

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|bn-a|<e

this inequality shows that b(n) has not reached the bound

what is the next step?

this inequality shows that b(n) has not reached the bound

what is the next step?

- #6

Office_Shredder

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So given e>0, can you find N such that n>N implies |b_{n}-a| < e?

- #7

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whats the role of "N"

why are you writing N>0 n>N ??

instead you could write just n>0

??

why are you writing N>0 n>N ??

instead you could write just n>0

??

- #8

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Think about what is going on in the sequence b. Are it's entries similar to those in a_n? What happens when you take a very large n?

- #9

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why in this example our N is 6?

the definition of a couchy sequesnse is:

after a finite number of steps, any pair chosen from the remaining terms will be within distance "e" of each other.

i can guess that for each bn

it take the largest member from a1 to an

for example:

a1=6 a2=5 a3=6 a4=1 a5=8 a6=7

b1=6 b2=6 b3=6 b4=6 b5=8 b6=8

what to do now?

the definition of a couchy sequesnse is:

after a finite number of steps, any pair chosen from the remaining terms will be within distance "e" of each other.

i can guess that for each bn

it take the largest member from a1 to an

for example:

a1=6 a2=5 a3=6 a4=1 a5=8 a6=7

b1=6 b2=6 b3=6 b4=6 b5=8 b6=8

what to do now?

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- #10

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anyone?

- #11

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why in this example our N is 6?

the definition of a couchy sequesnse is:

after a finite number of steps, any pair chosen from the remaining terms will be within distance "e" of each other.

N is 6 because after 6 steps, any pair of terms is "0" away from each other, so they are certainly less than "e" away from each other. So in general, N is the number of finite steps you must advance before "any pair chosen from the remaining terms will be within distance "e" of each other". This is more of an aid to visualize things and to keep things formal.

You may want to consult some of the theorems from real analysis like monotone convergence.

- #12

Office_Shredder

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The point of saying N>0 isn't to indicate that n>0 later, the point is that you have to pick a very large number (like you said, some finite number of steps). So given e>0, there exists N (whose value you don't know) such that n>N implies |a

- #13

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ok i understand after N step we have the members |bN-b(N+1)| < e

and when we take n>N its an over kill(to be absolutely sure)

and when we take n>N its an over kill(to be absolutely sure)

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- #14

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so i cant do this process

how to apply this process on my question?

- #15

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i am only given that sequence An converges to the value "a"

- #16

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i could say that if An s monotonic and converges then An+1 also converges to "a"

so Bn ->a

but here i cant say that An is monotonic

??

so Bn ->a

but here i cant say that An is monotonic

??

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