Recursion formula

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.

Related Introductory Physics Homework Help News on Phys.org

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

Homework Helper
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, an+1= (1/2)an.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving