Question

(50 PONTOS) Calcule o valor da seguinte soma:

$\displaystyle\sum\limits_{n=1}^{31}{n^{3/5}\cdot \left[\left(1+\dfrac{1}{n} \right )^{3/5}-1 \right ]}$
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Resposta: $7.$

Answer 1

Hola

$\displaystyle \sum\limits_{n=1}^{31}{n^{3/5}\cdot \left[\left(1+\dfrac{1}{n} \right )^{3/5}-1 \right ]}=\sum\limits_{n=1}^{31}(n+1)^{3/5}-n^{3/5}\\ \\ \\ =(31+1)^{3/5}-(1)^{3/5}=32^{3/5}-1=8-1=7$