(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)快
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![(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)快](/uploads/image/z/5904159-15-9.jpg?t=%281-1%2F2-1%2F3...-1%2F1996%29%2A%281%2F2%2B1%2F3%2B1%2F4%2B...%2B1%2F1997%29-%281-1%2F2-1%2F3...-1%2F1997%29%2A%281%2F2%2B1%2F3%2B1%2F4%2B...%2B1%2F1996%29%E5%BF%AB)
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(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)快
(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)
快
(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)快
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
换元法:令a=1/2+1/3...+1/1996,原式=(1-a)(a+1/1997)-(1-a-1/1997)×a=1/1997