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Core 2 Tommorow Need A Few Definitions Re-Capped...?

Basically in the sequence and series chapter I forgot the meaning of

Divergent

Convergent

could anybody offer a quick concise definition of these and how they apply to c2 questions thanks!
Reply 1
Avatar for kiran18
kiran18
Original post by mora11
Basically in the sequence and series chapter I forgot the meaning of

Divergent

Convergent

could anybody offer a quick concise definition of these and how they apply to c2 questions thanks!


if the sequence is diverging it will keep getting bigger and bigger or smaller and smaller
if it is converging it will get closer and closer to a certain point but never reach that point, this only happens is the common ratio(r) is between -1 and +1

this is all for geometric sequences
These only apply to geometric sequences.

A divergent sequence does not approach or tend to any value. This is generally when r > 1 and r < 1.

A converging sequence does the opposite, it approaches a value. This is generally when -1 < r < 1.
Reply 3
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mora11
OP
Original post by kiran18
if the sequence is diverging it will keep getting bigger and bigger or smaller and smaller
if it is converging it will get closer and closer to a certain point but never reach that point, this only happens is the common ratio(r) is between -1 and +1

this is all for geometric sequences


ok thanks for the recap but couldn't converging also be used to describe a arithmetic progression as well say for example if the common difference was 10 then the sequence would keep getting bigger?
Reply 4
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mora11
OP
Original post by I_Am_The_Man
These only apply to geometric sequences.

A divergent sequence does not approach or tend to any value. This is generally when r > 1 and r < 1.

A converging sequence does the opposite, it approaches a value. This is generally when -1 < r < 1.


k thanks for the recap but couldn't converging also be used to describe a arithmetic progression as well say for example if the common difference was 10 then the sequence would keep getting bigger?

and also I think you mean r>1 and r<-1 for divergent
Original post by mora11
k thanks for the recap but couldn't converging also be used to describe a arithmetic progression as well say for example if the common difference was 10 then the sequence would keep getting bigger?

and also I think you mean r>1 and r<-1 for divergent


Yes, sorry about that is what I meant and it could be applied in that way, but they would ask this question about a geometric sequence.
(edited 11 years ago)
Reply 6
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mora11
OP
Original post by I_Am_The_Man
Yes, sorry about that is what I meant and it could be applied in that way, but they would ask this question about a geometric sequence.


ok thanks mate!

good luck if your sitting any exams!

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