Question

calculati partea intreaga a numarului​

Answer 1

Răspuns:

$[a] = 1$

Explicație pas cu pas:

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

Answer 2

In atasament ai rezolvarea. Daca nu intelegi sa ma intreb.