求(1-1/2*2)+(1-1/3*3)+(1-1/4*4).+(1-1/2009*2009)_数学解答

求(1-1/2*2)+(1-1/3*3)+(1-1/4*4).+(1-1/2009*2009)

人气：493 ℃　时间：2020-04-15 16:01:59

解答

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