已知a=1，b=2，c=3，求1/abc+1/(a+1)(b+1)(c+1)+1/(a+2)(b+2)(c+2)+...1/(a+100)(b+100)(c+100)的值。
已知a=1，b=2，c=3，求1/abc+1/(a+1)(b+1)(c+1)+1/(a+2)(b+2)(c+2)+...1/(a+100)(b+100)(c+100)的值。
日期：2021-05-20 06:07:15 人气：1
代入a=1，b=2，c=3，有
1/a(a+1)(a+2)+1/(a+1)(a+2)(a+3)+...1/(a+100)(a+101)(a+102)
=1/1*2*3+1/2*3*4+1/3*4*5+...+1/101*102*103
注意到：
1/(a+n)(a+n+1)(a+n+2)
=1/(a+n)*1/(a+n+1)*1/(a+n+2)
=[1
1/a(a+1)(a+2)+1/(a+1)(a+2)(a+3)+...1/(a+100)(a+101)(a+102)
=1/1*2*3+1/2*3*4+1/3*4*5+...+1/101*102*103
注意到：
1/(a+n)(a+n+1)(a+n+2)
=1/(a+n)*1/(a+n+1)*1/(a+n+2)
=[1