Question

f:R->R , f(x)=2x-1 atunci f(1)+f(2)+f(3)+...+f(2007) este patrat perfect

Answer 1

f(1)      =2*1-1=1
f(2)      =2*2-1=3
f(3)      =2*3-1=5
....................
f(2007)=2*2007-1=4013
S = 1+3+5+ ... + 4013  folosim formula 1+3+5+...+2n-1=n²
in cazul nostru 2n-1=4013 => 2n=4014 => 4014:2 = 2007 ;
=> A = 1+3+5+ ... + 4013 = 2007²