1. Nov 27, 2011 #1

   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.

    

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   chooooch, Nov 27, 2011
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3. Nov 27, 2011 #2

   Dick

   

   Science Advisor

   Homework Helper

   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.

    

   Dick, Nov 27, 2011

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