# Infinite series proof

1. Oct 24, 2005

### happyg1

Hi,
I'm working on this problem:
If {s_n} is a nondecreasing sequence and s_n>=0, prove that there exists a series SUM a_k with a_k>=0 and s_n = a_1 + a_2 + a_3 + .......+ a_n.
I'm not sure where to start. I wrote out the sequence's terms:
s_n = (s_1, s_2, s_3, .....s_n)
Then I wrote;
s_1=a_1
s_2=a_1+a_2
.
.
s_n=a_1+a_2+......a_n
I'm unclear about exactly what I need to go for.
Any clarifiction will be greatly appreciated.
CC

2. Oct 24, 2005

### shmoe

Try to write the a's in terms of the s's. You've already got a_1=s_1. What must a_2 be? a_3? a_4? a_n?