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Razonamiento lógico 4. Si \( \sum_{i=1}^{30} a_{i}=170 \) y \( \sum_{i=1}^{100} a_{i}=470 \), halla \( \sum_{i=31}^{100} a_{i} \).

Ask by Frazier Nichols. in Colombia
Mar 14,2025

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La suma de los términos desde el 31 hasta el 100 es 300.

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Para resolver el problema, primero podemos utilizar las sumatorias proporcionadas. Dado que \( \sum_{i=1}^{100} a_{i}=470 \) nos dice el total de la suma de los primeros 100 términos, y \( \sum_{i=1}^{30} a_{i}=170 \) nos indica la suma de los primeros 30 términos, podemos encontrar la suma desde el término 31 hasta el término 100. Utilizamos la siguiente relación: \[ \sum_{i=31}^{100} a_{i} = \sum_{i=1}^{100} a_{i} - \sum_{i=1}^{30} a_{i} \] Sustituyendo los valores dados: \[ \sum_{i=31}^{100} a_{i} = 470 - 170 = 300 \] Por lo tanto, \( \sum_{i=31}^{100} a_{i} = 300 \).

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