Question

Can you help me understand the process for this question?

Answer 1

We are given the following series:

`\sum ^9_(k\mathop=0)\sin (\pi k)`

this means:

`\sin (\pi*0)+\sin (\pi*1)+\sin (\pi*2)+\sin (\pi*3)+\cdots+\sin (\pi*9)`

since the since of any multiple of pi is zero, this means that all these terms are zero, therefore, their sum is zero, this means:

`\sin (\pi k)=0\text{ for every k}`

therefore:

`\sum ^9_(k\mathop=0)\sin (\pi k)=0`