I will include my thought process as well..
Now we see that when an even m is a multiple of 4, its a + else it is a -
We can capture this idea by
When m is odd, anyway the expression is 0. The sign wont matter then. Thats why I choose
Where I have used the floor function on .
Thus
Note that functionally,
Thus a simplified form is:
Nice!
I should probably include my thought process as well.
I did not work off of the trig, rather I worked off of the sequence
I firstly saw that
gave
So I wanted then that for even value of n that ever other was positive.
So I saw that this was described by
A little less eloquent than Iso