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Evaluate the sum
First of all note that:
Hence letting we have that
Tags: Real Analysis, Series
Interesting remark: Let us consider the function
then we note that
Other interesting serieses of this form are:
Proof: We have successively:
Proof: We simply note that
Thus, the series telescopes.
Proof: The same as before note that the sum telescopes , since:
The result follows.
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