1. Let $A=\frac{21 \times 62+22 \times 63+23 \times 64+24 \times 65+25 \times 66}{21 \times 61+22 \times 62+23 \times 63+24 \times 64+25 \times 65} \times 199$, find the integer part of $\mathrm{A}$
【Answer】202
【Solution】First and last term approximation
$$
\begin{array}{l}
A=\frac{21 \times 61+21+22 \times 62+62+23 \times 63+63+24 \times 64+64+25 \times 65+65}{21 \times 61+22 \times 62+23 \times 63+24 \times 64+25 \times 65} \times 199 \\
=\left(1+\frac{21+62+63+64+65}{21 \times 61+22 \times 62+23 \times 63+24 \times 64+25 \times 65}\right) \times 199 \\
=199+\frac{21+62+63+64+65}{21 \times 61+22 \times 62+23 \times 63+24 \times 64+25 \times 65} \times 199
\end{array}
$$

Then $A199+\frac{21+22+23+24+25}{(21+22+23+24+25) \times 65} \times 199=199+\frac{199}{65}=202 \frac{4}{65}>202
$$

In summary, the integer part of $\mathrm{A}$ is 202