【Question 14】  
The Pythagorean school believed that numbers are the origin of all things, and they called numbers such as $1, 3, 6, 10, \cdots$ triangular numbers. If we arrange these triangular numbers in ascending order, the sum of the first 100 triangular numbers is $\qquad$.
【Analysis and Solution】
The $n$-th triangular number is $1+2+\cdots+n=(1+n) \times n \div 2$;
Therefore, the sum of the first 100 triangular numbers is
$$
\begin{array}{l}
(1+1) \times 1 \div 2+(1+2) \times 2 \div 2+\cdots+(1+100) \times 100 \div 2=(1 \times 2+2 \times 3+\cdots+100 \times 101) \div 2 \\
=[(1 \times 2 \times 3-0 \times 1 \times 2) \div 3+(2 \times 3 \times 4-1 \times 2 \times 3) \div 3+\cdots+(100 \times 101 \times 102-99 \times 100 \times 101) \div 3] \div 2 \\
=(100 \times 101 \times 102-0 \times 1 \times 2) \div 3 \div 2=100 \times 101 \times(102 \div 3 \div 2)=100 \times 101 \times 17=171700
\end{array}
$$