INDUKSI MATEMATIKA Buktikan: 1+4+7+...+(3n-2) = 1/2n (3n-1) jika n = 1 dan n = k+1 mohon jawaban disertai cara:)

Langkah 1

n = 1

3n-2 = 1/2 n (3n-1)
3(1) - 2 = 1/2 (1) (3(1)-1)
3 - 2  = 1/2 (2)
 1 = 1   TERBUKTI

Langkah 2

n = k

1+4+7+...+(3k-2) = 1/2k (3k-1)

Langkah 3

n = k+1

1+4+7+...+(3k-2) + (3(k+1)-2) = 1/2(k+1) (3(k+1)-1)
    1/2k (3k-1)    + 3k +1    =   (1/2k + 1/2) (3k + 2)
      3/2k² - 1/2k + 3k +1    =    3/2k² + k + 3/2k + 1
      3/2k² + 5/2k + 1          =    3/2k² + 5/2k + 1        TERBUKTI