write the sum without sigma notation. then evaluate. \n5\n∑ sin kπ\nk = 1

Explanation:

Step1: Expand the sum

$\sin(1\times\pi)+\sin(2\times\pi)+\sin(3\times\pi)+\sin(4\times\pi)+\sin(5\times\pi)$

Step2: Evaluate each term

We know that $\sin(n\pi)=0$ for all integers $n$. $\sin(\pi) = 0$, $\sin(2\pi)=0$, $\sin(3\pi)=0$, $\sin(4\pi)=0$, $\sin(5\pi)=0$

Step3: Calculate the sum

$0 + 0+0+0+0=0$

Answer:

$0$