# Homework Help: Proving the series divergent

1. Nov 27, 2011

### chooooch

1. The problem statement, all variables and given/known data

Suppose that ∑_(n=1)^∞▒a_n where a_n≠0 is known to be a convergent series. Prove that ∑_(n=1)^∞▒1/a_n is a divergent series.

2. Relevant equations

3. The attempt at a solution

if ∑_(n=1)^∞▒a_n is convergent then lim n→∞ a_n = 0. thus for some N a_n>1 and a_n >1/a_n if n>N. Thus, ∑_(n=1)^∞▒1/a_n diverges by comparison test.
I don't know if this is right, I don't know what to do.

#### Attached Files:

• ###### Untitled.png
File size:
4.8 KB
Views:
68
2. Nov 27, 2011

### Dick

A series can only converge if it's nth term approaches 0. You see this by looking at the limit of the partial sums. If limit a_n=0 then limit 1/a_n cannot be zero. As I think you were trying to say, for some N>0 and all n>N |a_n|<1. That would mean |1/a_n|>1.