Răspuns:
[tex][a] = 1[/tex]
Explicație pas cu pas:
[tex]\displaystyle a = 1 + \frac{1}{2} + \frac{1}{2^2} + \cdots + \frac{1}{2^9}\\\\\textrm{Putem aduce la acelasi numitor toate fractiile:}\\\\ a = \frac{2^9 + 2^8 + 2^7 + 2^6 + \cdots + 1}{2^9} = \frac{512 + 256 + 128 + \cdots + 1}{512}\\\\ = \frac{1023}{512}\\\\ = \frac{1024 - 1}{512}\\\\ = \frac{1024}{512} - \frac{1}{512}\\\\ = 2 - \frac{1}{512}\\\\\implies [a] = [2 - \frac{1}{512}] = 1[/tex]
