數學歸納法

題目應是 : 3x4+4x7+5x10+...+(n+2)(3n+1) = n(n+2)(n+3)當 n = 1 , (1+2)(3*1 + 1) = (1)(1 + 2)(1 + 3) = 12 命題正確。設當 n = k 時命題正確 :3x4+4x7+5x10+...+(k+2)(3k+1) = k(k+2)(k+3)當 n = k+1 時 :3x4+4x7+5x10+...+(k+2)(3k+1) + (k+3)(3(k+1) + 1)= k(k+2)(k+3) + (k+3)(3k+4)= (k+3) (k²+2k + 3k+4)= (k+3) (k²+5k+4)= (k+3) (k+1)(k+4)= (k+1) (k+3) (k+4) = (k+3) ( k(k+2) + (k+1)(k+4) )= (k+3) ( k² + 2k + k² + 5k + 4)= (k+3) (2k² + 7k + 4) 命題正確。由數學歸納法得證對於所有正整數n,命題正確。


2011-09-19 21:00:47 補充：
尾二至尾四行唔洗理。