Let denote the -th harmonic number and the -th harmonic number of order , namely . Prove that

**Solution**

**Lemma: **Let be a sequence such tht . Then

*Proof: *We have successively:

Thus,

Hence for the original problem if we let then

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Let denote the -th harmonic number and the -th harmonic number of order , namely . Prove that

**Solution**

**Lemma: **Let be a sequence such tht . Then

*Proof: *We have successively:

Thus,

Hence for the original problem if we let then