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
答
原式=(1-1/3+1/3-1/5+1/5-1/7……+1/2009-1/2011)/2
=(1-1/2011)/2
=(2010/2011)/2
=1005/2011
答
1/(1*3)=(1/2)(1-1/3)
1/3×5=(1/2)(1/3-1/5)
...
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
答
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