Răspuns:
f:R->R
f(x) =x-1/4
S=f(2¹)+f(2²)+...+f(2⁸)=
= (2¹-1/4) + (2²-1/4) +...+ (2⁸-1/4) =
= (2¹+2²+...+ 2⁸)-8*1/4
stim ca: 2+2²+2³+...+2ⁿ = 2ⁿ⁺¹ - 2
⇒ 2¹+2²+...+ 2⁸ = 2⁹ - 2
⇒ S = 2⁹- 2-2 =
= 2⁹- 4=
= 2⁹- 2²=
= 2²(2⁷- 1) =
= 4·(128-1) =
= 4·127 =
= 508
