The square wave has discontinuities at T/4 and +T/4. At either discontinuity, the Fourier Series converges to the mid point of the "jump". About either side of the jump the series oscillate. The height of the peaks of the oscillation decreases away from the jump, but the height of peak1, peak2 etc remain the same as the number of terms summed increases. The effect is referred to as the Gibbs phenomenon and is illustrated by the applet below. 
