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Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Geometric series

I'm looking at the series:

I have to find in what interval I it's convergent. I'm having trouble deciding if it's I=]0,1[, or I=[0,1[. If I write it 'out', I get:

Here's the problem. I say that it's a geometric series with a=1 and r=sqrt(x). We have that |r|<1 if it has to be convergent. This means:

Combined with x greater than or equal to 0, I get:

The thing I don't get though, is that if x is 0 (as allowed in my I) I get:

Which starts with an 0^0. Which leads me to I=]0,1[. Which is right? Or what am I missing? A definitionissue perhaps?

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G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: Geometric series

sqrt(x)<1 /2
x<1 if x<1 but you give that x>=0
so 0=<x<1

but

sqrt(x)<1/2
x>1 if x>1

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Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Geometric series

Thanks for taking the time to help, but I'm not sure what the last part means (after the but), and why you write sqrt(x) is less than a half?

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Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Geometric series

I found out, that 0^0 = 1, so my problems are solved

edit:(in this context)

Last edited by Patrick (2009-10-14 03:17:25)

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