Question

URGENT
Aratati ca numarul
a=5/4×9 + 7/9×16 + 9/16×25 + 11/25×36 apartine intervalului (1/9; 1/3)

Answer 1

Răspuns

Explicație pas cu pas:

$a=\frac{5}{4\cdot 9}+\frac{7}{9\cdot16}+\frac{9}{16\cdot 25}+\frac{11}{25\cdot 36}\\\\a=\frac{9-4}{4\cdot 9}+\frac{16-7}{9\cdot16}+\frac{25-16}{16\cdot 25}+\frac{36-25}{25\cdot 36}\\\\a=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{25}+\frac{1}{25}-\frac{1}{36}\\\\a=\frac{1}{4}-\frac{1}{36}= \frac{9-1}{36}=\frac{8}{36}=\frac{2}{9}\\\\\frac{1}{9}<\frac{2}{9}<\frac{1}{3} |\cdot 9\\\\1<2<3 - adevarat$