for $f(x)=x$ when $x∈[0,0.5]$
and $f(x)=1-x$ when $x∈(0.5,1]$
1-why Fourier "sine" series converges uniformly to f(x)?
2-Does it converge in $L^2$ sense?
My answer to the Question number 2, would be YES, because uniform convergence implies $L^2$ convergence. Am I correct? it there any contradiction case?
for the question Number 1, I am confused because of the word SINE. Would it differ the answer if it was Fourier series and not just Fourier sine series?
I know Weierstrauss M test, would you please help me make sure how to use that for this problem to prove uniform convergence?
Thank you