數學歸納法問題

when n=k+1
右方=(k+1)(k+2)^2............(*)
左方=1．4+2．7+3．10+．．．．．+ｋ(3ｋ＋1)+(k+1)(3k+4)............(**)
......=k(k+1)^2+(k+1)(3k+4)............(***)
......=(k+1)(k(k+1)+3k+4)
......=(k+1)(k^2+4k+4)
......=(k+1)(k+2)^2
P(k+1) is true if P(k) is true for any positive integer k
by principle of MI ,P(n) is true for all positive integers n

(*)在P(n)條式中右方代ｎ＝ｋ＋１
(**)在P(n)條式中左方代ｎ＝ｋ＋１時，由於佢只係加到n項,咁你就要幫佢加多個n+1項
記得要轉寫ｋ,但尼步唔一定要寫，如果係明，可以直接寫下步
(***)因為你已經假設左P(k) is true,所以你就將P(k)個result代入去

2007-09-15 19:16:18 補充：
k(k 1)^2 (k 1)(3k 4)let k 1=xkx^2 x(3k 4)x(kx 3k 4)抽通項

當n = k+1,
左方=1．4＋2．7＋3．10＋．．．．．＋ｋ（ 3ｋ＋1）+ (k+1)[3(k+1)+1]
＝ｋ（ｋ＋1）＾2 + (k+1)(3k+4)
=(k+1)(k^2+k+3k+4)
=(k+1)(k^2+4k+4)
=(k+1)(k+2)^2
=(k+1)[(k+1)+1]^2

所以p(k+1)成立

如下:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Sep07/CrazyMI25.jpg