Megoldások - 2024. modell (2023. nov.)

I.2

    f3(24) = 24*24/4 + 2*f3(12)
    f3(12) = 12*12/4 + 2*f3(6)
    f3(6) = 6*6/4 + 2*f3(3)
    f3(3) = 3 + f3(2)
    f3(2) = 2*2/4 + 2*f3(1)
    f3(1) = 1 + f3(0)
    f3(0) = 0

    f3(1) = 1
    f3(2) = 1 + 2 = 3
    f3(3) = 3 + 3 = 6
    f3(6) = 9 + 12 = 21
    f3(12) = 36 + 42 = 78
    f3(24) = 24*6 + 2*78
           = 4*36 + 4*39
           = 4*75
           = 300

    S(2n) = 2n*2n / 4 + 2*S(n)
    2n*(2n+1)/2 = n*n + n*(n+1)