# Need help finding the frequency response

So I have this system: $$y(n) = \frac{1}{N+1}\sum_{k=-N}^{N}\left(1-\frac{|k|}{N+1}\right)x(n-k)$$

Now for the impulse response I'm getting:

\begin{cases}\frac{1}{N+1}\left(1-\frac{|k|}{N+1}\right) &\text{for}\quad|n|\leq N\\ 0& \text{otherwise} \end{cases}

But now I'm supposed to find the frequency response and supposedly a closed form expression can be found for it.

So the frequency response is just the Fourier transform of the impulse response so I have this function:

$$F(s)=\frac{1}{p(N+1)}\sum_{k=-N}^{N}\left(1-\frac{|k|}{N+1}\right)e^{\frac{-2\pi isn}{p}}$$

From here I used Euler's formula and the $isin$ parts cancel themselves and then I was able to use Legendre's summation formulas to find a super messy closed form but I think that can't be right. I think instead I have set up the frequency response wrong. Could some one help me? Thanks.