Binomial Series Involving Harmonic-like Numbers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is suitable for publication but I would suggest the following issues:

1. The authors remark the difficulty to extend their analytical approach when the system become more complex.

2. The authors indicate a possible way to avoid the above problem: In this context it should be very nice to apply such suggested method to  some example already solved analytically.

3 Is there any numerical method to approach the sums, by comparing with the analytical expressions.

4. It would be nice to show some graphic of the convergence when the number of terms increase.

Author Response

see uploaded file "Response1Reviewer.pdf"

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please, see the attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Please, see the attached file.

Author Response

see uploaded file "Response2Reviewer.pdf"

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors need to redo the summary in a way that is easy to understand.

Author Response

The summary in Concluding Comments section is completely rewritten by explaining difficulties to evaluate the series containing harmonic numbers of higher order, and suggesting an alternative approach ""coefficient extraction". New examples are added to illustrate how to apply this alternative technique.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I agree with the changes in the paper and it is suitable for publication.