Suppose that f(x)= summation an x^n for n = 0 to infinity for all x. If f is an odd function, show that a0 = a2 = a4 = ... = 0.
The Attempt at a Solution
I said to consider sin(x), an odd function. When you do a series expansion only odd terms exist in the series so all even terms are equal to zero. This is because the nth derivative of sin(x) where n is an even number >= 2 always produces some form of cos(x) and when you plug 0 into cos(x) you get 0 and so even terms disappear. I was told that I restated the question and that I need to think harder about odd functions. I don't know how else to answer this. Thanks