1/n(n+1)(n+2)如何分解,分解成1/2（1/n(n+2)-1/(n+1)(n+2))的形式，

Question

1/n(n+1)(n+2)如何分解,
分解成1/2（1/n(n+2)-1/(n+1)(n+2))的形式，

Answer 1

1/[n(n+1)(n+2)]=1/2(1/[n(n+1)]-1/[(n+1)(n+2)])
证明方法就是右边同分.一般的想法是要能够分成形式上连贯的几项,所以把1/(n+1)保留在那2项里.
不是1/2(1/n(n+2)-1/(n+1)(n+2))而是1/n(n+2)-1/(n+1)(n+2)吧?