Răspuns:
ex.23
Explicație pas cu pas:
a)
[tex]\frac{^{2)} 1}{ {2}^{n - 1} } - \frac{1}{ {2}^{n} } = \frac{2 - 1}{{2}^{n}} = \bf \frac{1}{{2}^{n}} \\ [/tex]
b)
[tex]\frac{1}{2} - \Big(\frac{1}{{2}^{2}} + \frac{1}{{2}^{3}} + \frac{1}{{2}^{4}} + ... + \frac{1}{{2}^{10}}\Big) = \\ = \frac{1}{2} - \frac{1}{{2}^{2}} - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}}\\ = \Big(\frac{1}{2} - \frac{1}{{2}^{2}}\Big) - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{2}} - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} = ... = \bf \frac{1}{{2}^{10}}[/tex]
