Question

Fie f:R-R, a.) f(x) =2x-3, calculați f(1)+f(2)+...+f(30)

Answer 1

$f(1)+f(2)+\ldots +f(30)=\\ =2\cdot1-3+2\cdot 2-3+2\cdot 3-3+\ldots+2\cdot 30-3=\\ =2(1+2+\ldots+30)\underbrace{-3-3-\ldots-3}=\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~de\ 30\ ori\\ =2\cdot \dfrac{30\cdot 31}{2}-3\cdot 30=30\cdot 31-3\cdot 30=\boxed{840}$