Summing every ath term of a series using the roots of unity

Abstract

We give a simple method for finding the sum of every third (say) term of an analytic function. The main method uses the roots of unity. We also look at when these can be written in terms of square roots and cube roots.

Keywords:

• analytic functions
• roots
• series

Acknowledgements

The authors would like to thank the editor and the referee for their careful reading and for comments which improved the paper.