I'm trying to show the following argument but have a problem

If is the kth convergent of , show that for ,

I use that fact that

, and

etc,

we can see that is decreasing in steps.

But why instead of ?

Can anyone explain it to me? Thank you.

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- May 12th 2008, 06:04 PMkleenexNeed help on continued farction
I'm trying to show the following argument but have a problem

If is the kth convergent of , show that for ,

I use that fact that

, and

etc,

we can see that is decreasing in steps.

But why instead of ?

Can anyone explain it to me? Thank you. - May 12th 2008, 07:41 PMThePerfectHacker
This comes down to the inductive case . If was true then . But this is false because consider then .