Ta có : 12 - 22 + 32 - 42 + 52 - 62 + .... + 20192 - 20202
= (1 - 2)(1 + 2) + (3 - 4)(3 + 4) + (5 - 6)(5 + 6) + .... + (2019 - 2020)(2020 + 2019)
= -3 - 7 - 11 - ... - 4039
= - (3 + 7 + 11 + ... + 4039)
= - 1010.(4039 + 3) : 2
= - 1010.2021
= -2041210
\(=\left(2^2-1\right)+\left(4^2-3^2\right)+\left(6^2-5^2\right)+...+\left(2020^2-2019^2\right)=\)
\(=\left(2-1\right)\left(2+1\right)+\left(4-3\right)\left(4+3\right)+...+\left(2020-2019\right)\left(2020+2019\right)=\)
\(=3+7+11+....+4039=\frac{1009\left(4039+3\right)}{2}=\)
12 - 22 + 32 - 42 + ... + 20192 - 20202
= ( 12 - 22 ) + ( 32 - 42 ) + ... + ( 20192 - 20202 )
= ( 1 - 2 )( 1 + 2 ) + ( 3 - 4 )( 3 + 4 ) + ... + ( 2019 - 2020 )( 2019 + 2020 )
= (-1).3 + (-1).7 + ... + (-1).4039
= -3 - 7 - ... - 4039
= -( 3 + 7 + ... + 4039 )
= \(-\left(\frac{\left(4039+3\right)\left[\left(4039-3\right):4+1\right]}{2}\right)\)
= -2 041 210
