Exercise [1, p. 14 exercise 1.1] asks to prove that
g(x)=\frac{1}{1-x} (1)

is a monotonically increasing function over the interval 0<x<1. Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in  [1, Figure 1.2b] that they must also be present in the spectral estimate of [1, Figure 1.2a]. read the conclusion >