Problem

Source: China Northern MO 2008 p2 CNMO

Tags: Pascal's Triangle, algebra



The given triangular number table is as follows: Among them, the numbers in the first row are $1, 2, 3, ..., 98, 99, 100$. Starting from the second row, each number is equal to the sum of the left and right numbers in the row above it. Find the value of $M$.