Evaluate the sum

**Solution**

First of all note that:

Hence letting we have that

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Evaluate the sum

**Solution**

First of all note that:

Hence letting we have that

Interesting remark:Let us consider the functionthen we note that

Other interesting serieses of this form are:

1..Proof:We have successively:2..Proof:We simply note thatand

Thus, the series telescopes.

3..Proof:The same as before note that the sum telescopes , since:The result follows.