Question

用数学归纳法证明1*2*3+2*3*4+3*4*5+...+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4

Answer 1

以下用数学归纳法证明 1. 当n=1,左边1*2*3=6. 右边1*2*3*4/4=6. 明显成立 2.当n=k(k属于Z正) 也有1*2*3+2*3*4+.....+k(k+1)(k+2)=k(k+1)(k+2)(k+3)/4 当n=k+1时， 1*2*3+2*3*4+....+k(k+1)(k+2)+(k+1)(k+2)(k+3) =k(k+1)(k+2)(k+3)/4+(k+1)(k+2)(k+3) =k(k+1)(k+2)(k+3)/4+4(k+1)(k+2)(k+3)/4 =(k+1)(k+2)(k+3)(k+4)/4 即当n=k+1时，命题也成立. 由1.2可得，命题成立

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