Induksi Matematika

Buktikan : 2+ 5 + 8 . . . (3n-1) = n ( 3n + 1)/2

I.         n=1

3n-1          = n(3n+1)/2

2               = 2       ( terbukti)

II.      N=k

2+5+8 . . . ( 3k-1)                         = k(3k+1)/2

III.   N=k+1

2+5+8 . . . (3k-1)+( 3(k+1)-1)      = (k+1)(3(k+1)+1)/2

                

K(3k+1)/2            + (3(K+1)-1     =  (k+1)(3(k+1)+1)/2

K(3k+1)/2 + (3k+3-1) (disamakan Penyebut)=  (k+1)(3(k+1)+1)/2

K(3k+1)+6k+4/2                          =  (k+1) (3k+3)+1/2

K(3k+1)+6k+4/2                          =  (k+1) (3k+4)/2

3k² + k +6k+4/2                           =   3k² +4k+3k+4/2

3k² +7k+4/2                                  =  3k² +7k+4/2