Question

S=f(1) + f(2) + f(3) ...... f(100) f(x)=3x - 1
As dori o explicatie, va rog !

Answer 1

Răspuns:

Explicație pas cu pas:

f(x) = 3 x - 1

f(1) = 3 ×1 - 1 =>  f(1) = 2

f(2) = 3×2 - 1 => f(2) = 5

f(3) = 3 ×3 - 1 => f(3) = 8

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f(100) = 3 ×100 - 1 =>   f(100) = 299

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S = f(1) + f(2) + f(3) + ....... f(100)  -> 100 termeni are suma cu ratia=3

S = 2 + 5 + 8 + ...........+ 299

S = 100 × ( 2 + 299) : 2

S = 50 × 301

S = 15 050

Answer 2

Răspuns:

Explicație pas cu pas:

f(x)=3x - 1

S=f(1) + f(2) + f(3) ...... f(100)=???

Deoarece lui x i se dau valori naturale consecutive, fie x=a, atunci f(x+1)=a+1

Atunci f(a)=3·a-1, iar f(a+1)=3·(a+1)-1=3·a+3-1=3·a+2.

Deci f(a+1)-f(a)=3a+2-(3a-1)=3a+2-3a+1=3. Deci diferenta dintre termenii sirului f(1), f(2), f(3), ..., f(100) este o progresie aritmetica cu ratia 3.

Atunci S=f(1) + f(2) + f(3) ...... f(100)=100·(f(1)+f(100)):2

f(1)=3·1-1=2, f(100)=3·100-1=299. Atunci S=100·(2+299):2=50·301=15050