Question

Va rog punctele a) si b)!

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

a)

$\frac{1}{ {2}^{n - 1} } - \frac{1}{ {2}^{n} } = \frac{2}{2 \cdot {2}^{n - 1}} - \frac{1}{ {2}^{n} } = \frac{2 - 1}{{2}^{n}} = \red{\bf\frac{1}{ {2}^{n} }}$

b)

$\frac{1}{2} - (\frac{1}{ {2}^{2}} + \frac{1}{ {2}^{3}} + ... + \frac{1}{ {2}^{10}}) =$

$= \frac{1}{2} - \frac{1}{ {2}^{2}} - \frac{1}{ {2}^{3}} - ... - \frac{1}{ {2}^{10}}$

$= \left(\frac{1}{2} - \frac{1}{ {2}^{2}} \right) - \frac{1}{ {2}^{3}} - ... - \frac{1}{ {2}^{10}}$

$= \frac{1}{ {2}^{2}} - \frac{1}{ {2}^{3}} - ... - \frac{1}{ {2}^{10}}$

$= \left(\frac{1}{ {2}^{2}} - \frac{1}{ {2}^{3}} \right) - \frac{1}{ {2}^{4}} - ... - \frac{1}{ {2}^{10}}$

$= \frac{1}{ {2}^{3}} - \frac{1}{ {2}^{4}} - ... - \frac{1}{ {2}^{10}} = ... = \red{\bf \frac{1}{ {2}^{10}}}$