(1-1/2-1/3...-1/1996)*(1/2+1/3+1/4+...+1/1997)-(1-1/2-1/3...-1/1997)*(1/2+1/3+1/4+...+1/1996)

问题描述:

(1-1/2-1/3...-1/1996)*(1/2+1/3+1/4+...+1/1997)-(1-1/2-1/3...-1/1997)*(1/2+1/3+1/4+...+1/1996)

令A=1/2+1/3+1/4+...+1/1996
则原式子= (1-A)* (A + 1/1997) - (1-A - 1/1997 )* A
= (1-A)* A + (1-A)* 1/1997-(1-A)* A+ ( 1/1997 )* A
= (1-A)* 1/1997+ ( 1/1997 )* A
=1/1997