# Sequences and existence of limit

1. Nov 12, 2012

### Felafel

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

Let an be a bounded sequence and bn such that

the limit bn as n→∞ is b and

0<bn ≤ 1/2 (bn-1)

Prove that if:

an+1 ≥ an - bn,

then

lim an
n→∞

2. Relevant equations

3. The attempt at a solution

no clue :(
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 12, 2012

### micromass

Staff Emeritus

It's not possible to have "no clue". There are always things you can do:

• Write down the relevant definition such as convergence and bounded.
• Find a numerical example.
• What were some previous examples/problems where you had to show convergence, what were the steps you took there? Can you mimic those to an extent?

3. Nov 12, 2012

### micromass

Staff Emeritus
Also, please write out the full problem. Writing "then $\lim_{n\rightarrow +\infty} a_n$" is incomplete.

4. Nov 12, 2012

### Felafel

oops, sorry.
i'll write a new thread (properly)