Wenn f (1) = 3 und f (n) = -2f (n-1) + 1, was ist dann f (5)?

Antworten:

#f (5) = 43 #

Erläuterung:

#f (1) = 3 #

#f (n) = - 2f (n-1) + 1 #

#f (2) = - 2f (1) + 1 #

#f (2) = - 2 (3) + 1 = -6 + 2 = -5 #

#f (3) = - 2f (2) + 1 #

#f (3) = - 2 (-5) + 1 #

#f (3) = 11 #

#f (4) = - 2 (f (3)) + 1 #

#f (4) = - 2 (11) + 1 #

#f (4) = - 22 + 1 = -21 #

#f (5) = - 2 (f (4)) + 1 #

#f (5) = - 2 (-21) + 1 #

#f (5) = 42 + 1 #

#f (5) = 43 #