Σ (k = 0 bis n + 1) (k·f(k)) = (n + 1)·f(n + 1 + 2) - f(n + 1 + 3) + 2
Σ (k = 0 bis n) (k·f(k)) + (n + 1)·f(n + 1) = (n + 1)·f(n + 3) - f(n + 4) + 2
n·f(n + 2) - f(n + 3) + 2 + (n + 1)·f(n + 1) = (n + 1)·f(n + 3) - f(n + 4) + 2
n·f(n + 1) + n·f(n + 2) - n·f(n + 3) + f(n + 1) + f(n + 4) - 2·f(n + 3) = 0
n·(f(n + 1) + f(n + 2) - f(n + 3)) + f(n + 1) + f(n + 4) - 2·f(n + 3) = 0
nutze f(n + 1) + f(n + 2) = f(n + 3) --> f(n + 1) = f(n + 3) - f(n + 2)
n·(f(n + 3) - f(n + 3)) - f(n + 2) + f(n + 4) - f(n + 3) = 0
nutze - f(n + 2) - f(n + 3) = - f(n + 4)
n·(f(n + 3) - f(n + 3)) + f(n + 4) - f(n + 4) = 0