1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013

1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013

1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013
=（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+…… +1/2011-1/2013）÷2
=（1-1/2013）÷2
=2012/2013÷2
=1006/2013

1+3+5+7+.+2011+2013

1+3+5+7+.+2011+2013
=[(1+2013)/2]²
=1007²
=1014049

Simplify 1 / √ 3 + 1 + 1 / √ 5 + √ 3 + 1 / √ 7 + √ 5 + +1/√2013+√2011

1 / radical 3 + 1 + 1 / radical 5 + radical 3 + 1 / radical 7 + radical 5 1 / radical 2n + 1 + radical 2N-1
=(1/2)[√3-1+√5-√3+√7-√5+…… +√（2n+1）-√(2n-1)]
=(1/2)(√（2n+1）-1)
And bring 2013 in
The original formula = (√ 3-1) / 2 + (√ 5 - √ 3) / 2 + (√ 7 - √ 5) / 2 + +[√(2n+1)-√(2n-1)]/2
=[√3-1+√5-√3+√7-√5+…… +√(2n+1)-√(2n-1)]/2
=[√(2n+1)-1]/2

1 in 2014 + 2 in 2014 + 3 in 2014 +. + 2013 in 2014
How to write. Quick, urgent

=1 of 2014 * (1 + 2 + 3 +... + 2013)
=1 of 2014 * (1 + 2013) * 2013 / 2
=2013/2
=1006.5

Calculation: 1 / 2-1 / + / 1 / 3-1 / 2 / + / 1 / 4-1 / 3 / +. + / 2014 / 1-2013 / 1/

Original formula = 1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 + +1/2013-1/2014
=1-1/2014
=2013/2014