5) Recall that the Fourier series of the sawtooth function x, x E [- 1, 1 ) S a = f (a + 2) is given by 2/T E (-1)n+1 n sin (wnx) . n=1 i) Show that the Fourier series of s converges for every x, i.e., SN() - S* (x). ii ) Show that SN(1 - ~) - 2/7 Jo sin(x) / xdx. iii ) Using power series expansion of sin (xx), show that 2/7 , sin(x) /xdx > 1.17. iv) Why the fact that limN- SN(1 - ~) > 1.17 does not contradict the convergence of the Fourier series of the sawtooth function for every x