Question

tính nhanh 1²-2²+3²-4²+..........+99²-100²

Answer 1

\(\left(1^2-2^2\right)+\left(3^2-4^2\right)+....+\left(99^2+100^2\right)\)

Answer 2

\(\left(1^2-2^2\right)+\left(3^2-4^2\right)+....+\left(99^2-100^2\right)\)

=\(\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+....+\left(99-100\right)\left(99+100\right)\)

=\(-1\left(1+2\right)+\left(-1\right)\left(3+4\right)+....+\left(-1\right)\left(99+100\right)\)

=\(-\left(1+2+3+....+99+100\right)\)

=\(-\dfrac{\left(1+100\right).100}{2}=-101.50=-5050\)