數學歸納法

當 n = 1 , 2 (1) (3(1) - 1) = 2 (1)² (1+1) = 4 , 命題正確。假設當 n = k 時命題正確:2x2 + 4x5 + 6x8 + ... 2k(3k-1) = 2k² (k+1)當 n = k + 1 時 ,2x2 + 4x5 + 6x8 + ... 2k(3k-1) + 2(k+1)(3(k+1) - 1) = 2k² (k+1) + 2(k+1)(3(k+1) - 1) = 2(k+1) (k² + (3(k+1) - 1)= 2 (k + 1) (k² + 3k + 2)= 2 (k + 1) (k + 1)(k + 2)= 2 (k + 1)² (k + 2) 命題正確。由數學歸納法得證對於所有正整數 n , 命題正確。