# Tricky calculus question - i've got problems

• herraotic
In summary, the conversation discusses a proof for the divergence of a series with a general term of min(an, 1/n), where (an) is a sequence of positive real numbers that are decreasing and have an infinite sum. The conversation also mentions that the proof involves showing that the sequence is monotonic decreasing.

#### herraotic

Let (an) 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(an, 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!

herraotic said:
Let (an) 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(an, 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

nth term -> min (an or 1/n)

for nth+1 term -> min (an+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

an+1 < an

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

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