= Solution
Evenness removes every sine coefficient. In the period-two <Fourier cosine series> convention $f=a_0/2+\sum_{n\geq1}a_n\cos(n\pi x)$, the constant coefficient is $a_0=2\int_0^1(1-x)dx=1$. <Integration by parts> gives
$$
a_n=2\int_0^1(1-x)\cos(n\pi x)dx=\frac{2[1-(-1)^n]}{n^2\pi^2}.
$$
Thus the <Fourier cosine series of a triangular wave> is
$$
\boxed{f(x)=\frac12+\frac4{\pi^2}\sum_{m=0}^\infty\frac{\cos((2m+1)\pi x)}{(2m+1)^2}.}
$$
The periodic function is continuous and piecewise smooth, so the <Dirichlet-Jordan convergence theorem> gives its value at every point. The summable absolute coefficient bound also gives <uniform convergence> by the <Weierstrass M-test>.
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