Đáp án:
$\begin{array}{l}
P = \left( {{2^2} + {4^2} + {6^2} + ... + {{100}^2}} \right)\\
- \left( {{1^2} + {3^2} + {5^2} + ... + {{99}^2}} \right)\\
= \left( {{2^2} - {1^2}} \right) + \left( {{4^2} - {3^2}} \right) + \left( {{6^2} - {5^2}} \right) + .. + \left( {{{100}^2} - {{99}^2}} \right)\\
= \left( {2 - 1} \right).\left( {2 + 1} \right) + \left( {4 - 3} \right).\left( {4 + 3} \right)\\
+ \left( {6 - 5} \right)\left( {6 + 5} \right) + ... + \left( {100 - 99} \right)\left( {100 + 99} \right)\\
= 1.\left( {1 + 2} \right) + 1.\left( {3 + 4} \right) + 1.\left( {5 + 6} \right) + ... + 1.\left( {99 + 100} \right)\\
= 1 + 2 + 3 + 4 + 5 + 6 + ... + 99 + 100\\
= \dfrac{{\left( {100 + 1} \right).100}}{2}\\
= 5050
\end{array}$
