5. (1 mark) A positive integer is said to be a "palindrome" if it reads the same from left to right as from right to left. For example 2002 is a palindrome. Find the sum of all 4-digit palindromes.
(1 分) A positive integer is said to be a "palindrome" if it reads the same from left to right as from right to left. For example 2002 is a palindrome. Find the sum of all 4-digit palindromes.
5. Each 4-digit palindrome is of the form $\overline{a b b a}$, where $a$ ranges from 1 to 9 and $b$ from 0 to 9. Hence the sum of all 4-digit palindromes is equal to $\sum_{n=0}^{9} \sum_{m=1}^{9}(1001 m+110 n)$ $=\sum_{n=0}^{9}(1001 \times 45+110 n \times 9)=1001 \times 45 \times 10+45 \times 9 \times 110=11000 \times 45=\underline{\underline{495000}}$.