计算1/1×3+1/3×5+1/5×7...+1/2009×2011

问题描述:

计算1/1×3+1/3×5+1/5×7...+1/2009×2011

1/1×3=1/2×(1/1-1/3)1/3×5=1/2×(1/3-1/5)1/5×7=1/2×(1/5-1/7).1/2009×2011=1/2×(1/2009-1/2011)所以原式=1/2×(1-1/3+1/3-1/5+...+1/2009-1/2011)=1/2×(1-1/2011)=1005/2011