Question

Se considera functia f:R->R,f(x)=x^2-6x+10
Sa se calculeze suma f(1)+f(2)+...+f(20)

Answer 1

f(1) e 1^2 -6*1 +10
f(2) e 2^2 -6*2 +10
f(3) e 3^2 -6*3 +10
...
f(20) e 20^2 -6*20 +10

f(1)+f(2) + ... f(20)=
se grupeaza si vine
1^2 + 2^2 + 3^2 +...+20^2 -6(1+2+3...+20) + 10*20=
prima e formua primelor n patrate
20*(20+1)*(2*20+1)/6 -6*20*21/2 +200=
20*21*41/6 - 3*20*21+200=
se da factor comun 20
20(21*41/6  -63 +10)=
20(21*41/6 -53)
21 se simplifica cu 6 prin 3

20(7*41/2 +10)
20 * (287/2+10)=
20*(287/2 +20/2)=

20 * 307/2 =307*10=3070