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

• April 22nd 2011, 01:01 AM
ahm0605
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.
• April 22nd 2011, 02:09 AM
girdav
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.
• April 23rd 2011, 11:53 PM
ahm0605
What is geq and neq
• April 24th 2011, 12:33 AM
FernandoRevilla
Quote:

Originally Posted by ahm0605
What is geq and neq

Greater or equal and not equal .
• April 24th 2011, 01:51 AM
girdav
Quote:

Originally Posted by ahm0605
What is geq and neq

I will edit this post when LaTeX will work. I hope it's understandable.
• May 3rd 2011, 08:35 AM
girdav
Well I write again my first post.
We can find a strictly increasing sequence of integer $(n_k)$ such that $q_{n_k}\geq k$. Put $a_{n_k}=\frac 1{kq_{n_k}}$ and $a_j=0$ if $j\neq n_k$ for all $k$.