Question

tính giá trị của biểu thức \(1^2-2^2+3^2-4^2+.....+99^2-100^2+101^2\)

Answer 1

\(1^2-2^2+3^2-4^2+.................+99^2-100^2+101^2\)

\(=\left(-3\right)+\left(-7\right)+\left(-11\right)+........+\left(-199\right)+10201\)

\(=\frac{50.\left[\left(-199\right)+\left(-3\right)\right]}{2}+10201\)

\(=\left(-5050\right)+10201\)

\(=5151\)

Answer 2

\(1^2-2^2+3^2-4^2+...+99^2-100^2+101^2\)

\(=\left(-3\right)+\left(-7\right)+\left(-11\right)+...+-199+101^2\)

\(=\frac{50\left(-199+\left(-3\right)\right)}{2}+10201\)

\(=-5050+10201\)

\(=5151\)