# Series problem

Find a series of real numbers {an} such that a1+ a2+a3+...=-1 and a1+3 a2+5 a3+...+(2n-1)an+...=0.
Also there have to be an infinite number of non-zero ans.

I'm not sure how to begin this. Can it be done?

## Answers and Replies

I like Serena
Homework Helper
Find a series of real numbers {an} such that a1+ a2+a3+...=-1 and a1+3 a2+5 a3+...+(2n-1)an+...=0.
Also there have to be an infinite number of non-zero ans.

I'm not sure how to begin this. Can it be done?

Suppose you subtract the first series from the second.
See any pattern?