Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
1 - 5 - 9 + 13 + 17 - 21 - 25 + 29 + ...... + 2001 - 2005 - 2009 + 2013\\
= \left( {1 - 5} \right) - \left( {9 - 13} \right) + \left( {17 - 21} \right) - \left( {25 - 29} \right) + ..... + \left( {2001 - 2005} \right) - \left( {2009 - 2013} \right)\\
= - 4 + 4 - 4 + 4 - ...... - 4 + 4\\
= 0\\
b,\\
P - Q = \frac{{2010}}{{2011}} + \frac{{2011}}{{2012}} + \frac{{2012}}{{2013}} - \frac{{2010 + 2011 + 2012}}{{2011 + 2012 + 2013}}\\
= \frac{{2010}}{{2011}} + \frac{{2011}}{{2012}} + \frac{{2012}}{{2013}} - \frac{{2011 + \left( {2010 + 2012} \right)}}{{2012 + \left( {2011 + 2013} \right)}}\\
= \frac{{2010}}{{2011}} + \frac{{2011}}{{2012}} + \frac{{2012}}{{2013}} - \frac{{2011 + 2.2011}}{{2012 + 2.2012}}\\
= \frac{{2010}}{{2011}} + \frac{{2011}}{{2012}} + \frac{{2012}}{{2013}} - \frac{{3.2011}}{{3.2012}}\\
= \frac{{2010}}{{2011}} + \frac{{2012}}{{2013}} > 0\\
\Rightarrow P > Q
\end{array}\)
