fourier

Hello everyone, I have issue understanding two conclusion made byDr. Baker in his mixed signal books as shown in page 35 and 36. 1- how can using the convulution yield from euation 2.8 to 2.9 . I applied the convultion to it and I get double summation and not as in equation 2.9! 2-the equation...

So i am trying to calculate the fourier transform of this waveform. I have made an attempt at it but i dont think its right: S(t) = 1000t The integral of: 1000t*e^-jwt dt , with the limits: 0 to 1x10^-3