Recursion Formula for Series: a (n) = 1/2^n

[hamsterbrs]

Can you write the recursion formula for this series?'
a (then little n) = 1/2^n

*the 2 is to the nth power, not the one
*for the first half, it is written a then a little n to the bottom right.

I don't understand how to even go about this. Any help would be great thanks.

 

[da_willem]

$$a_n =\frac{1}{2^n}$$

Write down some of the terms like $a_0 =\frac{1}{2^0}, a_1=\frac{1}{2^1}, a_2=...$ using this formula. Now a recursion relation is a relation that relates a term ($a_n$) in this series to the previous term ($a_{n-1}$). You are asked to find this relation. If you see the pattern in the terms it shouldn't be too difficult to write down $a_n$ in terms of $a_{n-1}$.

 

[HallsofIvy]

First write out a few of those numbers and look at them!
$$1, \frac{1}{2},\frac{1}{4},\frac{1}{8}...$$

Now think "how do you go from one number to the next?" (that's what recursion IS!). Looks to me like you multiply by 1/2!

That is: a₀= 1, a_n+1= (1/2)a_n.