I see in your post a statement of a function and a statement of the Taylor polynomial, along with some conclusions about derivatives.
But what are you supposed to be proving?
Let
by taylor series: =
So
... where when n is odd and when n is even.
Differentiating w.r.t (t) =
when n=2,t =1, give
when n=4, t=1, give
and so on
This is quite obvious but i have difficulty putting in word to show that
when n is odd and
when n=2j
Any better way to show?