 In fact, Euler held that this series obeyed the formal relation Σ cos "kx" = −1⁄2, while d'Alembert rejected the relation, and Lagrange wondered if it could be defended by an extension of the geometric series similar to Euler's reasoning with Grandi's numerical series.Euler's claim suggests that

for all "x".This series is divergent everywhere, while its Cesàro sum is indeed 0 for almost all "x".