3. Let $r \geqslant 4, a=\frac{1}{r}-\frac{1}{r+1}$,
$$
b=\frac{1}{\sqrt{r}}-\frac{1}{\sqrt{r+1}}, c=\frac{1}{r(\sqrt{r}+\sqrt{r+1})} \text {. }
$$

Then among the following options, the one that must be true is ( ).
(A) $a>b>c$
(B) $b>c>a$
(C) $c>a>b$
(D) $c>b>a$
3. D.

Since $r \geqslant 4$, we have $\frac{1}{\sqrt{r}}+\frac{1}{\sqrt{r+1}}\frac{\sqrt{r+1}-\sqrt{r}}{\sqrt{r} \cdot \sqrt{r+1}}=\frac{1}{\sqrt{r}}-\frac{1}{\sqrt{r+1}}=b .
\end{array}
$

Therefore, $c>b>a$.