Question

Stabiliți dacă x€(1/4;1/3).
$x = \frac{4}{3 \times 7} + \frac{5}{7 \times 12} + \frac{6}{12 \times 18} + \frac{7}{18 \times 25} \:$
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Answer 1

Răspuns:

Explicație pas cu pas:

4/3·7=1/3-1/7

5/7·12=1/7-1/12

6/12·18=1/12-1/18

7/18·25=1/18-1/25

.................................

   x=1/3-1/25=(25-3)/75=22/75=0,29(3)

1/4=0,25      si 1/3=0,(3)

⇒0,25<x<0,333

Answer 2

Răspuns:

DA, apartine, mie așa mi-a dat!

Explicație pas cu pas:

• 4/3*7= 4/3*(3+4)= 4*(1/4)*(1/3-1/7)=1/3-1/7 ***

• 5/7*12=...=5*(1/5)*(1/7-1/12) =1/7-1/12

• 6/12*18=.....=68(1/6)* (1/12-1/18)=1/12-1/18

• 7/18*25=..= 7*(1/7) (1/18-1/25)=1/18-1/25

insumand,  obtinem

• 1/3-1/25<1/3

si

• 1/3-1/25= (25-3)/75= 22/75>22/88=1/4

• deci x∈(1/4;1/3)

***am folosit relatia, usor de demonstrat

1/n(n+k)=(1/k)*(1/n- 1/(n+k))