# Thread: q_1, q_2, ... , q_n, ... is a sequence of real numbers

1. ## q_1, q_2, ... , q_n, ... is a sequence of real numbers

q_1, q_2, ... , q_n, ... is a sequence of real numbers such that the limit of q_n, as n goes towards infinity, is +infinity.

Show that we can find a sequence a_1, a_2, ... , a_n, ... sych that the sum(a_n) is convergent but the sum(a_n*q_n) is divergent.

2. We can find a stricly increasing sequence of integer (n_k) such that q_{n_k}\geq k. Put a_{n_k}=1/(kq_{n_k}) and a_j=0 if j\neq n_k for all k.

3. What is geq and neq

4. Originally Posted by ahm0605
What is geq and neq

Greater or equal and not equal .

5. Originally Posted by ahm0605
What is geq and neq
I will edit this post when LaTeX will work. I hope it's understandable.

6. Well I write again my first post.
We can find a strictly increasing sequence of integer $\displaystyle (n_k)$ such that $\displaystyle q_{n_k}\geq k$. Put $\displaystyle a_{n_k}=\frac 1{kq_{n_k}}$ and $\displaystyle a_j=0$ if $\displaystyle j\neq n_k$ for all $\displaystyle k$.