230问答网 > 计算 (1-1⼀2^2 )(1-1⼀3^2 )(1-1⼀4^2 )…(1-1⼀2002^2 )(1-1⼀2003^2 )

计算 (1-1⼀2^2 )(1-1⼀3^2 )(1-1⼀4^2 )…(1-1⼀2002^2 )(1-1⼀2003^2 )

2024-12-12 02:06:25

推荐回答（2个）

回答1：

回答2：

(1-1/2^2 )(1-1/3^2 )(1-1/4^2 )…(1-1/2002^2 )(1-1/2003^2 )
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)…(1-1/2002 )(1+1/2002 )(1-1/2003 )(1+1/2003 )
=(1-1/2 )(1-1/3 )…(1-1/2002 )(1-1/2003 )*(1+1/2 )(1+1/3 )…(1+1/2002 )(1+1/2003 )
=(1/2*2/3*3/4*…*2001/2002*2002/2003)*(3/2*4/3*5/4*…*2003/2002*2004/2003)
=1/2003*2004/2=1002/2003