Question

Fie functia f: R-> R , f(x)= 2x-8 Calculati:

a) f(1) + f(2) + f(3) + f(4) + f(5) +...+ f(2014)
b) f(1) x f(2) x f(3) x f(4) x f(5) x...x f(2014)

Answer 1

a) f(1) + f(2) + f(3) + f(4) + f(5) +...+ f(2014)=
-6+-4+-2+0+2+4+6+8+10+12+...+4020=
8+10+12+...+4020=suma gauss
4028*2007/2=2014*2007 =............




b) f(1) x f(2) x f(3) x f(4) x f(5) x...x f(2014) =-6x-4x-2x0x2x4x........=0

Answer 2

a) f(1) + f(2) + f(3) + f(4) + f(5) +...+ f(2014)=(f(1)+ f(2014))x2014/2
=(-4+4020)x1007=4044112

b) f(1) x f(2) x f(3) x f(4) x f(5) x...x f(2014)=0  (pentru ca f(4)=0)