Question

Calcule os somatório ​

Answer 1

Calculando os somatórios, temos:

$\bf \sum\limits_{n=1}^{5} ( a_{n} + 1) =\boxed{\bf ( a_{1} + 1 ) + ( a_{2} + 1) + (a_{3} + 1) + (a_{4} + 1) + ( a_{5}+1)}$

$\bf\sum\limits_{n=1}^5\left(\dfrac{2n}{3}\right)=\boxed{\bf10}$

Um somatório, é uma abreviação de uma soma enorme . Para calcular, deve-se substituir o indice n por 1 até chegar no número de cima. Logo:

• Item a)

$\bf \sum\limits_{n=1}^{5} ( a_{n} + 1) =\boxed{\bf ( a_{1} + 1 ) + ( a_{2} + 1) + (a_{3} + 1) + (a_{4} + 1) + ( a_{5}+1)}$

• Item b)

$\bf \sum\limits_{n=1}^{5} \left(\dfrac{2n}{3} \right) = \left(\dfrac{2\cdot 1}{3} \right) + \left(\dfrac{2\cdot 2}{3} \right) + \left(\dfrac{2\cdot 3}{3} \right) + \left(\dfrac{2\cdot 4}{3} \right) + \left(\dfrac{2\cdot 5}{3} \right) \\\\\\ \bf \sum\limits_{n=1}^{5} \left(\dfrac{2n}{3} \right) = \left(\dfrac{2}{3} \right) + \left(\dfrac{4}{3} \right) + \left(\dfrac{6}{3} \right) + \left(\dfrac{8}{3} \right) + \left(\dfrac{10}{3} \right)$

$\bf\sum\limits_{n=1}^5\left(\dfrac{2n}{3}\right)=\left(\dfrac{2+4+6+8+10}{3}\right)\\\\\\\bf\sum\limits_{n=1}^5\left(\dfrac{2n}{3}\right)=\left(\dfrac{30}{3}\right)\\\\\\\bf\sum\limits_{n=1}^5\left(\dfrac{2n}{3}\right)=\boxed{\bf10}$

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