1. Mar 9, 2008

### mercedesbenz

1. The problem statement, all variables and given/known data
Let $$u_n, v_n$$ be a sequence of positive real number such that
$$u_{n+1}\leq (1+v_n)u_n$$ where $$\sum_{n=1}^{\infty}v_n$$
converges.

if $$\frac{u_{n+1}}{u_n}\leq M$$ then $$u_n\leq M$$
for some $$M$$ be a positive real number.

whether we can find $$M$$ is a positive real number such that
$$u_n\leq M$$ for all natural number n

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution