Please could you expand on this....why have you separated the and how do I proceed after?
Do exactly as I wrote: take the limit in both sides when ...
I represented (not separated) as I did above so that we'll be able to evaluate the sequence's limit.
Do exactly as I wrote: take the limit in both sides when ...
I represented (not separated) as I did above so that we'll be able to evaluate the sequence's limit.
Tonio
So, evaluate
Am I ok to drop the modulus' when evaluating the limit as above?
I'm not sure how to evaluate this
To say that means .
So the sequence is a Cauchy sequence.
That means we can make .
That is sufficient to prove the property:
So proscientia's post shows the sequence is Cauchy, right?
And as you've stated the distance but since as in a Cauchy sequence, that implies it must tend to zero....is my thinking right?
So proscientia's post shows the sequence is Cauchy, right?
And as you've stated the distance but since as in a Cauchy sequence, that implies it must tend to zero....is my thinking right?
No, but close: since the sequence (of partial sums of the series) is Cauchy then it has a limit, but since the limit of equals the limit of and since, as I wrote in the first message, , then...