(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
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(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2010)(1+1/2010)
=1/2×3/2×2/3×4/3×3/4×5/4×...×2009/2010×2011/2010
=1/2×2011/2010
=2011/4020