因式分解(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2006^2)如题,
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因式分解(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2006^2)如题,
因式分解(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2006^2)
如题,
因式分解(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2006^2)如题,
原式=(1²-1/2²)(1²-1/3²)(1²-1/4²)……(1²-1/2006²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2006)(1-1/2006)
=3/2·1/2·4/3·2/3·5/4·3/4……2007/2006·2005/2006
=(3/2·4/3·5/4……2007/2006)(1/2·2/3·3/4……2005/2006)
=2007/2·1/2006
=2007/4012
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2006^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)....(1-1/2006)(1+1/2006)
=1/2*3/2*2/3*.....2005/2006*2007/2006
=1/2*2007/2006
=2007/4012