Tricky calculus question - i've got problems

[herraotic]

Let (a_n) be a sequence of positive real numbers, decreasing and the sum of whose terms is infinite. Prove that the series whose general term is min(a_n, 1/n) is also divergent.

I'm sorry but I'm no where with it. Could someone tell me if this is too difficult?

Thanks!

 

[Roni1985]

Let (a_n) be a sequence of positive real numbers, decreasing and the sum of whose terms is infinite. Prove that the series whose general term is min(a_n, 1/n) is also divergent.

I'm sorry but I'm no where with it. Could someone tell me if this is too difficult?

Thanks!

I think that all you have to show here is that it is a monotonic decreasing sequence

n^th term -> min (a_n or 1/n)

for n^th+1 term -> min (a_n+1 or 1/(n+1))

the 'min' function says that you choose 1/n or something lower than 1/n

so you can tell for sure that

a_n+1 < a_n

 

[herraotic]

I'm still stumped. Why don't you let me off and show the solution :D :D ;D