So after the half range fourier series of sinx i have got the left hand side.
But my teachers answer has got this on the right how do i get it to equal this?
Lets work with the inside for now,
Note that if then the above must equal 0. So n must be even, which means
This gives us
So my answer will be,
Is this the same as theres? Lets change it around
If you sub in into their equation and mine you arrive at
So I think they are equal. let's equate them
Note how these are the same if n=even!
However, if n=odd the right side is equal to 0, which is the same result as I achieved, however i had the stipulation before making my equation that n cannot be odd.
Thus, left side = right side!