Question

tính bằng cách hợp lí :

\(\frac{1}{2001\times2003}+\frac{1}{2003\times2005}+\frac{1}{2005\times2007}+.....+\frac{1}{2009\times2011}+\frac{1}{2011\times2013}\)

Answer 1

Giúp mình nha

Answer 2

Ta có: 1/ 2001 . 2003 = 1/2001 - 1/2003...

=> 1/2001 - 1/2003 + 1/2003 - 1/2005 + 1/2005 - 1/2007 + ... +1/2009 - 1/2011 +1/2011 - 1/2013

= 1/2001 - 1/2013

= 4/ 1342671

Answer 3

\(\frac{1}{2001\times2003}\)+\(\frac{1}{2003\times2005}\)+\(\frac{1}{2005\times2007}\)+........+\(\frac{1}{2009\times2011}\)+\(\frac{1}{2011\times2013}\)

=\(\frac{1}{2001}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2007}\)+........+\(\frac{1}{2009}\)-\(\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2013}\)

=\(\frac{1}{2001}\)-\(\frac{1}{2013}\)

=\(\frac{2013}{4028013}-\frac{2001}{4028013}\)=\(\frac{2}{4028013}\)

Answer 4

\(\frac{1}{2001\cdot2003}\)+ \(\frac{1}{2003\cdot2005}\)+ \(\frac{1}{2005\cdot2007}\)+ ........ + \(\frac{1}{2011\cdot2013}\)

= \(\frac{1}{2}\)( \(\frac{1}{2001}\)- \(\frac{1}{2003}\)+ \(\frac{1}{2003}\)- \(\frac{1}{2005}\)+ ...... + \(\frac{1}{2011}\)-\(\frac{1}{2013}\))

=\(\frac{1}{2}\)( \(\frac{1}{2001}\)- \(\frac{1}{2013}\)) = \(\frac{1}{2}\)\(\frac{2}{4004013}\)= \(\frac{1}{4004013}\)

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