Question

-1+2-3+4...-201+202=?

Answer 1

$-1+2-3+4...-201+202 =\\ \\= (2-1)+(4-3)+(6-5)+...+(202-201) =\\ \\ = (\bold{1}\times 2-1)+(\bold{2}\times 2-3)+(\bold{3}\times2-5)+...\\ ...+(\bold{101}\times2-201) =\\ \\ =1+1+1+\underset{\text{de 101 ori}}{\underbrace{...}}+1 = \\ \\ = 1\times 101 = 101$