Question

E(0)+E(1)+E(2)+......+E(100) = CUM SE FACE ???

 

Answer 1

$E(x)=-x^2+x+1$
Atunci suma se scrie
$E(0)+\displaystyle\sum_{k=1}^{100}(-k^2+k+1)=\\=1-\sum_{k=1}^{100}k^2+\sum_{k=1}^{100}k+100$
Se folosesc sumele
$\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}{6}, \ \sum_{k=1}^nk=\frac{n(n+1)}{2}$