# Math Series

1. Jan 4, 2012

### mtayab1994

1. The problem statement, all variables and given/known data

$$U_{n+1}=\sqrt{12+U_{n}}$$ V0=0

2. Relevant equations
1) prove that Un<4
2) prove that $$4-U_{n+1}\leq\frac{1}{4}(4-U_{n})$$
3) conclude that 4-Un<(1/4)^(n-1)

3. The attempt at a solution

1- for n=0 0<4
assume Un<4 for some n in N and prove that Un+1<4

√(12+Un)<4 then square both sides and we get:

12+Un<16 then Un<4
so for every n in N: Un<4

2) I don't know what to do any help?

2. Jan 4, 2012

### obafgkmrns

2) I don't know what to do any help?

Have you tried substituting √(12+Un) for U(n+1) in $$4-U_{n+1}\leq\frac{1}{4}(4-U_{n})$$ and then evaluating the resulting expression for the largest possible value of U(n+1)?

3. Jan 4, 2012

### mtayab1994

Yea i just did that thanx for your help