1. ## sequences...

$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n+1}}$
$\displaystyle n\geq 0$
$\displaystyle a_0=1$

I need to write $\displaystyle a_{n+1}$ in terms of $\displaystyle \frac{1}{2}a_n$

I've written out the first few terms... but I'm just not seeing it... apparently this is a geometric sequence if that helps...

Thanks.

Also, while I'm here, what's the TeX code to put a space? Cheers

2. Originally Posted by Aileys.
$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n+1}}$
$\displaystyle n\geq 0$
$\displaystyle a_0=1$

I need to write $\displaystyle a_{n+1}$ in terms of $\displaystyle \frac{1}{2}a_n$

I've written out the first few terms... but I'm just not seeing it... apparently this is a geometric sequence if that helps...

Thanks.

Also, while I'm here, what's the TeX code to put a space? Cheers
Question - Is it

$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n+1}},\;\;n\geq 0,\;\;a_0=1$

or

$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n}},\;\;n\geq 0,\;\;a_0=1$

As for spaces, the easiest is using \, (small) or \; (regular)

3. Originally Posted by Danny
Question - Is it

$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n+1}},\;\;n\geq 0,\;\;a_0=1$

or

$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n}},\;\;n\geq 0,\;\;a_0=1$

As for spaces, the easiest is using \, (small) or \; (regular)
It says $\displaystyle a_{n+1}=a_n+\frac{1}{2^{n+1}},\;\;n\geq 0,\;\;a_0=1$... but maybe it's a typo... can you answer the question if it's
$\displaystyle a_{n+1}=a_n+\frac{1}{2^{n}},\;\;n\geq 0,\;\;a_0=1$? I still can't :S