If $\sum_{i=1}^\infty a_i$ diverges, then prove that $\sum_{i=1}^\infty ia_i$ diverges.
My English is too bad to express the question clearly. Thank you for your answer.
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Rd.Fu
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Hello and welcome. Your english is actually total okay and I can understand your question. What have you tried so far and where did you got stuck? – Dec 08 '16 at 09:03
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I have tried proofs by contradiction and order test,but I failed.Then I have no idea what to do next. – Rd.Fu Dec 08 '16 at 09:09
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Can you provide a proof in detail?I had failed so much times.This question almost drived me crazy. – Rd.Fu Dec 08 '16 at 09:12
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Are the terms positive, or not necessarily? – StackTD Dec 08 '16 at 09:15
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not necessarily – Rd.Fu Dec 08 '16 at 09:16
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Thank you for your answer.I've got it. – Rd.Fu Dec 08 '16 at 09:29