Question

f:R->R
f(x) = 6- x
Calculati: a) f(1) + f(2) + f(3) + ..... + f(100)
b) f(1)*f(2)*f(3)*....*f(10)

Answer 1

a.
f(1) = 6-1 = 5
f(2) = 6-2 = 4
f(3) = 6-3 = 3
f(4) = 6-4 = 2
f(5) = 6-5 = 1
f(6) = 6-6 = 0
....
f(100) = 6-100 = -94

f(1) + f(2) + f(3) + ..... + f(100)= 5+4+3+2+1+0-1-2-...-94
= 5+4+3+2+1 - (1+2+3+..94)
= 15 - [94*(94+1)]/2
= 15 - 4465
= - 4450

b.
f(1)*f(2)*f(3)*....*f(10) 
cum f(6) = 6-6=0 => f(1)*f(2)*f(3)*....*f(10) =0