tugas portofolio Algoritma

1) Basis step 4^n -1 habis dibagi 3untuk setiap bilangan bulat
S(1) = benar n>=1
S(n) = s(1)
4^n-1 = 4^1 – 1 , habis dibagi 3 (benar)

2) Inductive step
S(k) = benar
S(n) = S(k)
n=k
4^n – 1 = 4^k – 1 ……..(1)
S(k+1) = benar
S(n) = S(k+1)
n=k+1
4^n -1 = 4^k – 1
= 4^k * 4 -1
= 4 * 4^k – 1
S(k), S(k=1) = benar
3*4^k + 4^k – 1 …….( habis dibagi 3 ) berarti (benar)