Question
6. Hallar el valor \( \quad \sum_{k=1}^{4}\left(\frac{1}{k}+k\right) \)
Ask by Washington Pena. in Colombia
Mar 15,2025
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Answer
La suma es \( \frac{145}{12} \).
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Para resolver la suma \( \sum_{k=1}^{4} \left(\frac{1}{k} + k\right) \), lo descomponemos en dos partes: 1. \( \sum_{k=1}^{4} \frac{1}{k} \) que se evalúa como \( 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} \), lo cual suma aproximadamente \( 2.0833 \). 2. \( \sum_{k=1}^{4} k \) que es simplemente \( 1 + 2 + 3 + 4 = 10 \). Ahora sumamos ambas partes: \[ 2.0833 + 10 = 12.0833.\] Entonces, el valor de la suma es aproximadamente \( 12.0833 \).