1/1x3+1/3x5+1/5x7+…+1/2009x2011 急

1/1x3+1/3x5+1/5x7+…+1/2009x2011 急
1/1x3+1/3x5+1/5x7+…+1/2009x2011 急

1/1x3+1/3x5+1/5x7+…+1/2009x2011 急
1/1x3+1/3x5+1/5x7+…+1/2009x2011
=(1/1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+...+(1/2009-1/2011)/2
=(1/1-1/2011)/2
=1005/2011

1/1x3+1/3x5+1/5x7+……+1/2009x2011
=1/2(2/1x3+2/3x5+2/5x7+……+2/2009x2011)
=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/2009-1/2011)
=1/2x(1-1/2011)
=2010/4022