Question

Calculati suma S=f(1)+f(2)+...f(10), unde functia f : R--> R este data de legea de corespondenta indicata:

a) f(x)=7 b) f(x)=x-2 c) f(x)=-2x+1 d) f(x)=4x

Va rog repede.

Answer 1

a.  f(x) = x - 2 
     f(1) = 1 - 2 = - 1
     f(2) = 2 - 2 = 0
     f(3) = 3 - 2 = 1
     f(4) = 4 - 2 = 2
     f(5) = 5 - 2 = 3
     f(6) = 6 - 2 = 4
     f(7) = 7 - 2 = 5
     f(8) = 8 - 2 = 6
     f(9) = 9 - 2 = 7
     f(10) = 10 - 2 = 8
 
     s = f(1) + f(2) + .... + f(10)
     s = - 1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
     s = 35

b.  f(x) = - 2x + 1
     f(1) = -2×1 + 1 = - 2 + 1 = - 1
     f(2) = -2×2 + 1 = - 4 + 1 = - 3
     f(3) = -2×3 + 1 = - 6 + 1 = - 5
     f(4) = -2×4 + 1 = - 8 + 1 = - 7
     f(5) = -2×5 + 1 = - 10 + 1 = - 9
     f(6) = -2×6 + 1 = - 12 + 1 = - 11
     f(7) = -2×7 + 1 = - 14 + 1 = - 13
     f(8) = -2×8 + 1 = - 16 + 1 = - 15
     f(9) = -2×9 + 1 = - 18 + 1 = - 17
     f(10) = -2×10 + 1 = - 20 + 1 = - 19
   
     s = f(1) + f(2) + .... + f(10)
     s = - 1 - 3 - 5 - 7 - 9 - 11 - 13 - 15 - 17 - 19
     s = - 100

c.  f(x) = 4x
     f(1) = 4 × 1 = 4
     f(2) = 4 × 2 = 8
     f(3) = 4 × 3 = 12
     f(4) = 4 × 4 = 16
     f(5) = 4 × 5 = 20
     f(6) = 4 × 6 = 24
     f(7) = 4 × 7 = 28
     f(8) = 4 × 8 = 32
     f(9) = 4 × 9 = 36
     f(10) = 4 × 10 = 40
   
     s = f(1) + f(2) + .... + f(10)
     s = 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 + 40
     s = 220

Cel mai bun raspuns?