Cho A = \(\frac{1}{3^2} + \frac{3}{3^4} + \frac{5}{3^6} + \ldots + \frac{99}{3^{100}}. \) Chứng minh \( A < \frac{5}{32} \)

----- Nội dung ảnh -----
Cho A = \(\frac{1}{3^2} + \frac{3}{3^4} + \frac{5}{3^6} + \ldots + \frac{99}{3^{100}}. \) Chứng minh \( A < \frac{5}{32} \).