依照规律计算:1/1×3+1/3×5+1/5×7+...+1/2013×2015
2个回答

1/1×3+1/3×5+1/5×7+...+1/2013×2015

=2×(1/1×3+1/3×5+1/5×7+...+1/2013×2015)÷2

=(2/1×3+2/3×5+2/5×7+...+2/2013×2015)÷2

=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/2011-1/2013+1/2013-1/2015)÷2

=(1-1/2015)÷2

=2014/2015÷2

=1007/2015