Let be a fifth root of unity

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

Let α\alpha be a fifth root of unity, where α≠1\alpha\ne1. Then find the value of α[1+∑k=1∞αk(1−α)(1−α2)⋯(1−αk)].\alpha\left[1+\sum_{k=1}^{\infty}\alpha^k(1-\alpha)(1-\alpha^2)\cdots(1-\alpha^k)\right].

Related theory

Browse the problem library