Question

Tính: A = -1²+2² - 3² + 4² - ... - 99²+100²

Answer 1

A = -1² + 2² - 3² + 4² - ... - 99² + 100²

= (2²-1²) + (4²-3²) + ...+ (100²-99²)

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

= 1 + 2 + 3 + ... + 100

= \(\dfrac{100.101}{2}=5050\)

Vậy A = 5050

Answer 2

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

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

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

\(\Leftrightarrow A=1+2+3+....+100\)

\(\Leftrightarrow A=\dfrac{100.101}{2}=5050\)

Answer 3

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

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

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

\(A=1+2+3+....+100\)

\(A=\left[\left(\dfrac{100-1}{1}\right)+1\right]:2\left(100+1\right)=5050\)