\(M=1^2-2^2+3^2-4^2+...-2016^2+2017^2\)
\(=\left(2017^2-2016^2\right)+...+\left(3^2-2^2\right)+1^2\)
\(=\left(2017-2016\right)\left(2017+2016\right)+...+\left(3-2\right)\left(3+2\right)+1\)
\(=2017+2016+...+3+2+1\)
\(=\frac{2017\cdot\left(2017+1\right)}{2}=2035153\)
\(M=1^2-2^2+3^2-4^2+...-2016^2+2017^2\)
\(=\left(1^2-2^2\right)+\left(3^2-4^2\right)+...+\left(2015^2-2016^2\right)+2017^2\)
\(=\left(1+2\right)\left(1-2\right)+\left(3+4\right)\left(3-4\right)+...+\left(2015+2016\right)\left(2015-2016\right)+2017^2\)
\(=\left(1+2\right)\cdot\left(-1\right)+\left(3+4\right)\cdot\left(-1\right)+...+\left(2015+2016\right)\cdot\left(-1\right)+2017^2\)
\(=\left(-1\right)\cdot\left(1+2+...+2016\right)+2017^2\)
\(=\left(-1\right)\cdot\frac{2016\cdot\left(2016+1\right)}{2}+2017^2\)
\(=-2033136+4068289=2035153\)
Mình lại không thích bóng đá nhưng lại thích đá bóng,làm thế nào tính,
M= (20172 -20162) + (20152 -20142) +........+ (32-22) +12
M=(2017-2016)(2017+2016)+(2015-2014)(2015+2014)+........+(3-2)(3+2)+1
M=2017+2016+..........+3+2+1
M=\(\frac{2017\cdot\left(2017+1\right)}{2}\)= 2035153
