(1-1⼀4)*(1-1⼀9)*……*(1-1⼀2009^)

2024-12-20 15:57:18
推荐回答(1个)
回答1:

平方差公式
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2009)(1-1/2009)
=3/2×1/2×4/3×2/3……2010/2009×2008/2009
=(3/2×4/3……2010/2009)×(1/2×2/3……2008/2009)
=2010/2×1/2009
=1005/2009