Question

se considera functia f:R-R, f(x)= 2x+1. Sa se demonstreza ca numarul a= f(0)+f(1)+f(2)+...+f(10) este patrat perfect

Answer 1

a=(2·0+1)+(2·1+1)+(2·2+1)+...+(2·10+1)=2·0+2·1+2·2+...+2·10+1+1+...+1=
2(0+1+2+...+10)+11=2·10*11/2+11=10·11+11=11(10+1)=11·11=11² (patrat perfect)