Question

Ajutati-ma la exercitiul 34!
va rog!

Answer 1

   
[tex]\displaystyle \left(\frac{1}{88}+ \frac{1}{808}+\frac{1}{8008}+ \hdots +\frac{1}{8\underbrace{000\cdots00}_{n~zerouri}8} \right) \cdot x = \\ \\ = \frac{1}{44}+ \frac{1}{404}+\frac{1}{4004}+ \hdots +\frac{1}{4\underbrace{000\cdots00}_{n~zerouri}4} \\ \\ \text{La primul sir, dam factor comun pe }~ \frac{1}{2} [/tex]



[tex]\displaystyle \frac{1}{2} \left(\frac{1}{44}+ \frac{1}{404}+\frac{1}{4004}+ \hdots +\frac{1}{4\underbrace{000\cdots00}_{n~zerouri}4} \right) \cdot x = \\ \\ = \frac{1}{44}+ \frac{1}{404}+\frac{1}{4004}+ \hdots +\frac{1}{4\underbrace{000\cdots00}_{n~zerouri}4} \\ \\ \text{Observam ca cele doua sume sunt egale. }[/tex]



[tex]\displaystyle x= \frac{ \frac{1}{44}+ \frac{1}{404}+\frac{1}{4004}+ \hdots +\frac{1}{4000\cdots004} }{ \frac{1}{2} \left(\frac{1}{404}+\frac{1}{4004}+ \hdots +\frac{1}{4000\cdots004}\right)}= \frac{1}{\frac{1}{2}} = \boxed{2}[/tex]