99^2+99*2+1=? 40^2-39^2+38^2-37^2+……..+2^2-1^2 2019^2-2018*2020 23/09/2021 Bởi Audrey 99^2+99*2+1=? 40^2-39^2+38^2-37^2+……..+2^2-1^2 2019^2-2018*2020
\[\begin{array}{l} a)\,\,\,{99^2} + 2.99 + 1 = {\left( {99 + 1} \right)^2} = {100^2} = 10000.\\ b)\,\,{40^2} – {39^2} + {38^2} – {37^2} + ….. + {2^2} – {1^2}\\ = \left( {{{40}^2} – {{39}^2}} \right) + \left( {{{38}^2} – {{37}^2}} \right) + …. + \left( {{2^2} – {1^2}} \right)\\ = \left( {40 – 39} \right)\left( {40 + 39} \right) + \left( {38 – 37} \right)\left( {38 + 37} \right) + …. + \left( {2 – 1} \right)\left( {2 + 1} \right)\\ = 40 + 39 + 38 + 37 + …. + 2 + 1\\ = \frac{{40\left( {40 + 1} \right)}}{2} = 20.41 = 820.\\ c)\,\,\,{2019^2} – {2018^2} = \left( {2019 – 2018} \right)\left( {2019 + 2018} \right)\\ = 4037. \end{array}\] Bình luận
a)992+2.99+1=(99+1)2=1002=10000.b)402−392+382−372+.....+22−12=(402−392)+(382−372)+....+(22−12)=(40−39)(40+39)+(38−37)(38+37)+....+(2−1)(2+1)=40+39+38+37+....+2+1=40(40+1)2=20.41=820.c)20192−20182=(2019−2018)(2019+2018)=4037 Bình luận
\[\begin{array}{l}
a)\,\,\,{99^2} + 2.99 + 1 = {\left( {99 + 1} \right)^2} = {100^2} = 10000.\\
b)\,\,{40^2} – {39^2} + {38^2} – {37^2} + ….. + {2^2} – {1^2}\\
= \left( {{{40}^2} – {{39}^2}} \right) + \left( {{{38}^2} – {{37}^2}} \right) + …. + \left( {{2^2} – {1^2}} \right)\\
= \left( {40 – 39} \right)\left( {40 + 39} \right) + \left( {38 – 37} \right)\left( {38 + 37} \right) + …. + \left( {2 – 1} \right)\left( {2 + 1} \right)\\
= 40 + 39 + 38 + 37 + …. + 2 + 1\\
= \frac{{40\left( {40 + 1} \right)}}{2} = 20.41 = 820.\\
c)\,\,\,{2019^2} – {2018^2} = \left( {2019 – 2018} \right)\left( {2019 + 2018} \right)\\
= 4037.
\end{array}\]
a)992+2.99+1=(99+1)2=1002=10000.b)402−392+382−372+.....+22−12=(402−392)+(382−372)+....+(22−12)=(40−39)(40+39)+(38−37)(38+37)+....+(2−1)(2+1)=40+39+38+37+....+2+1=40(40+1)2=20.41=820.c)20192−20182=(2019−2018)(2019+2018)=4037