Question

se a pertence a N e a<5, qual é a soma dos números da forma sem (a.pi/2)?

Answer 1

Olá Nicoly!

Resposta:

$\boxed{\mathtt{Zero}}$

Explicação passo-a-passo:

De acordo com o enunciado, $\displaystyle \mathtt{a \in \mathbb{N}}$ e $\displaystyle \mathtt{a < 5}$.

Isto posto, temos que: $\displaystyle \mathtt{a = \left \{ 0, 1, 2, 3, 4 \right \}}$.

Com efeito,

$\\ \displaystyle \mathsf{\sum_{a = 0}^4 \sin \left (a \cdot \frac{\pi}{2} \right ) = \sin \left ( 0 \cdot \frac{\pi}{2} \right ) + \sin \left ( 1 \cdot \frac{\pi}{2} \right ) + \sin \left ( 2 \cdot \frac{\pi}{2} \right ) + \sin \left ( 3 \cdot \frac{\pi}{2} \right ) + \sin \left ( 4 \cdot \frac{\pi}{2} \right )} \\\\\\ \mathsf{\sum_{a = 0}^4 \sin \left (a \cdot \frac{\pi}{2} \right ) = \sin 0 + \sin \frac{\pi}{2} + \sin \pi + \sin \frac{3\pi}{2} + \sin 2\pi} \\\\\\ \mathsf{\sum_{a = 0}^4 \sin \left (a \cdot \frac{\pi}{2} \right ) = 0 + 1 + 0 + (- 1) + 0} \\\\\\ \boxed{\boxed{\mathsf{\sum_{a = 0}^4 \sin \left (a \cdot \frac{\pi}{2} \right ) = 0}}}$