D= $\frac{3}{1^2.2^2}$+ $\frac{5}{2^2.3^2}$+ $\frac{7}{3^2.4^2}$+...+ $\frac{19}{9^2.10^2}$
=(1-$\frac{1}{4}$)+ ($\frac{1}{4}$- $\frac{1}{9}$)+ ($\frac{1}{9}$- $\frac{1}{16}$)+...+ ($\frac{1}{81}$- $\frac{1}{100}$)
=1-$\frac{1}{4}$+ $\frac{1}{4}$- $\frac{1}{9}$+ $\frac{1}{9}$- $\frac{1}{16}$+...+ $\frac{1}{81}$- $\frac{1}{100}$
= 1-$\frac{1}{100}$
=$\frac{99}{100}$
$\frac{99}{100}$=0,99<1 ⇒ D<1