Limiting Sum (1 Viewer)

[laters]

Hi,

I have a question about conditions of the limiting sum formula ...

The condition is that |r|<1 but I'd just like to clarify whether r=0 should be included in this, because my teacher explained it as a literal limit i.e. your series will approach S but never actually reach it... but with r=0, your series has already reached this sum (i.e. S=a)

So for questions such as "Find x such that has a limiting sum", do I include tanx=0 in my solution?

 

[Silly Sausage]

You can write it as ?

 

[laters]

You can write it as ?

Yes I know the solution should go like
etc.

I just wanted to know whether tanx=0 should be included... i.e. using my thoughts above I might get -1<tanx<0, 0<tanx<1

 

[InteGrand]

You include 0

 

[braintic]

There is no issue with limits actually being reached. For example, lim(x->1) x is a valid question.
But for the limiting sum of a GP, it really is a degenerate case.

 

[laters]

There is no issue with limits actually being reached. For example, lim(x->1) x is a valid question.
But for the limiting sum of a GP, it really is a degenerate case.

Thanks for the clarification