COMB(n, k) + COMB(n, k + 1) = COMB(n + 1, k + 1)
n!/(k!·(n - k)!) + n!/((k + 1)!·(n - k - 1)!) = (n + 1)!/((k + 1)!·(n - k)!)
n!·(k + 1)/(k!·(k + 1)·(n - k)!) + n!·(n - k)/((k + 1)!·(n - k - 1)!·(n - k)) = (n + 1)!/((k + 1)!·(n - k)!)
n!·(k + 1)/((k + 1)!·(n - k)!) + n!·(n - k)/((k + 1)!·(n - k)!) = (n + 1)!/((k + 1)!·(n - k)!)
n!·(k + 1) + n!·(n - k) = (n + 1)!
n!·(k + 1 + n - k) = (n + 1)!
n!·(n + 1) = (n + 1)!
(n + 1)! = (n + 1)! --> stimmt