Question

Aflati nEn astfel incat fractia 18/n+7 sa fie:
a) echiunitara b) supraunitara c)subunitara

2. Simplificati fractia 111+444-222/222.

3.Simplificati fractia 2+4+6+.,...140/3+6+9+....+210

Answer 1

n∈N
18/n+7
a. 18/n+7 = 1
18=n+7
n=11
S={11}
b. 18/n+7>1
18>n+7
11>n
S={12, 13, 14.....}
c. 18/n+7<1
18<n+7
11<n
S={0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10}

2.(111+444-222)/222=333/222=3/2 (simplificata cu 111)

3. numaratorul= 2+4+6+....+140=2(1+2+3+....70)
   numitorul = 3+6+9+...+210=3(1+2+3+....+70)
fractia=2(1+2+3+...+70)/3(1+2+3+...+70)=2/3 (simplificata prin toata paranteza)
daca vrei poti calcula paranteza
1+2+3+...+n=n(n+1)/2=70·71/2=35·71=2485