Question

Fie functia f:|R cu valori in |R,f (x)=2x-3.Sa se calculeze f (1)+f (2)+....f (100)=?

Answer 1

$f(1)+f (2)+....+f (100)=-1+1+2+3+5+7+...+197 = \\ 1+3+5+7+...+197+1= \\ \\ 1+3+5+7+...+n = (\frac{n+1}{2})^{2} \\ \\=(\frac{197+1}{2})^{2} +1 = (\frac{198}{2})^{2} +1 = 99^{2} +1 = 9802$