P1 - Cálculo 4 - 2023-1

5, d_1 d_2 d_3 d_4 d_5 = \frac{d_1}{10} + \frac{d_2}{10^2} + \frac{d_3}{10^3} + \frac{d_4}{10^4} + \ldots = \sum_{i=1}^{\infty} \frac{d_i}{10^i} onde d_i = \{ 0, 1, 2, \ldots, 9 \} Pelo critério da razão: \quad a_i = \frac{d_i}{10^i} \left| \frac{a_{i+1}}{a_i} \right| = \left| \frac{d_{i+1}}{10^{i+1}} \cdot \frac{10^i}{d_i} \right| = \left| \frac{d_{i+1}}{d_i} \cdot \frac{10^i}{10^{i+1}} \right| = \left| \frac{d_{i+1}}{d_i} \cdot \frac{1}{10} \right| < 1 \quad \lambda \quad d_i \neq 0