Cho A = \(\frac{1}{7^2} - \frac{1}{7^4} + \frac{1}{7^6} - \frac{1}{7^8} + \ldots + \frac{1}{7^{98}} - \frac{1}{7^{100}} \). CM: A < \(\frac{1}{50}\)

Chứng minh. làm rõ từng bước.
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1, Cho A = \(\frac{1}{7^2} - \frac{1}{7^4} + \frac{1}{7^6} - \frac{1}{7^8} + \ldots + \frac{1}{7^{98}} - \frac{1}{7^{100}} \). CM: A < \(\frac{1}{50}\).