Sequences and existence of limit

[Felafel]

Homework Statement

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→∞

Homework Equations

The Attempt at a Solution

no clue :(

 

[micromass]

Please provide an attempt or this thread will be locked.

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?

 

[micromass]

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

 

[Felafel]

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