Question

Fie functia f:R - R, f(x) = x + 1.
Aratati ca numarul A = 2012 + 2 × [f(0) + f(1) + ... + f(2010)] este patrat perfect.
Va roog! E urgent!!

Answer 1

$f(0)+f(1)+...+f(2010)=1+2+...+2011= \frac{2011*2012}{2} \\ \\ A=2012+2* \frac{2011*2012}{2}=2012+2011*2012=2012(1+2011)= \\ =2012*2012= 2012^{2}-patrat~perfect.$

Answer 2

f(0)+f(1)+...+f(2010)=1+2+...+2011=2011*2012/2
2[suma]=2*2011*2012/2=2011*2012
A=2012+2011*2012=2012(1+2011)=2012*2012=2012² care este patrat perfect