原式 = [1 – (1/2) 2 ][1 –(1/3) 2 ] [1 – (1/4) 2 ]……[1 – (1/2011) 2 ][1 – (1/2012) 2 ] = (1 – 1/2)(1 + 1/2)* (1 – 1/3)(1 + 1/3)* (1 – 1/4)(1 + 1/4)*……*(1 – 1/2011)(1 + 1/2011)* (1 – 1/2012)(1 + 1/2012) = (1/2)*(3/2)*(2/3)*(4/3)*(3/4)*……*(2013/2012) = 2013/4024,即原式 = 2013/4024 .