Weierstrass M-test
General · Mathematics
Study notes
Q: Show Σ(sin(nx)/n²) converges uniformly on ℝ. |sin(nx)/n²| ≤ 1/n² = Mₙ. ΣMₙ = Σ1/n² converges (p=2!)! M-test: Σsin(nx)/n² converges UNIFORMLY (and absolutely!) on ℝ! (Sum is continuous - uniform limit of continuous!)