(1+1/2)*(1+1/4)*(1+1/5)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)怎么简便计算?

(1+1/2)*(1+1/4)*(1+1/5)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)怎么简便计算?
(1+1/2)*(1+1/4)*(1+1/5)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)怎么简便计算?

(1+1/2)*(1+1/4)*(1+1/5)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)怎么简便计算?
(1+1/2)*(1+1/4)*(1+1/6)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/7)*……*(1-1/9)
=3/2×5/4×7/6×9/8×11/10×2/3×4/5×6/7×8/9
=3/2×2/3×5/4×4/5×7/6×6/7××9/8×8/9×11/10
=11/10
前部分分母是2、4、6、8、10,后部分分子是3、5、7、9,除1+1/10,可配成4对倒数.
原题中1-1/6应为1-1/7

(1+1/2)*(1+1/4)*(1+1/6)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)
=【(1+1/2)*(1-1/3)】*【(1+1/4)*(1-1/5)】*【(1+1/6)*(1-1/7)】*……*【(1+1/8)(1-1/9)】(1+1/10)
=1*1*1*1*11/10
=11/10

(1+1/2)*(1+1/4)*(1+1/5)*……*(1+1/10)*(1-1/3)*(1-1/5)*(1-1/6)*……*(1-1/9)
=3/2*5/4*6/5*……*11/10*2/3*4/5*5/6*……*8/9
=(3/2*2/3)*(5/4*4/5)*（6/5*5/6)*……(9/8*8/9)* 11/10
=11/10