1/1.3+1/3.5+1/5.7+...=1/2009.2011
=1/2.(1-1/3+1/3-1/5+1/5-1/7+...+1/2009-1/2011)
=1/2.(1-1/2011)
=1/2.2010/2011
=1005/2011
Gọi tổng trên là A
2A = 2/1.3 + 2/3.5 + 2/5.7 +......+ 2/2009.2011
2A = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +..........+ 1/2009 - 1/2011
2A = 1 - 1/2011
2A = 2010/2011
A = 1005/2011
Vậy................
=1/2(1/1-1/3+1/3-1/5+...-1/2011)
=1/2(1-1/2011)
=1005/2011
1/2(1-1/3+1/3-1/5+1/5-1/7+.......+1/2009-1/2011)
=1/2(1-1/2011)
=1/2.2010/2011
=1005/2011
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7.......-1/2009+1/2009-1/2011)
=1/2*(1-1/2011)
=1/2*2010/2011
=1005/2011
1/1*3+1/3*5+...+1/2009*2011
=1/2*(1-1/3+1/3-1/5+1/5-1/7+...+1/2009-1/2011)
=1/2*(1-1/2011)
=1/2*2010/2011
=1005/2011
