Question

23.a)calculati 1/2^n-1 - 1/2^n.
b)folosind rezultatul de la punctul a) ,calculati: 1/2-(1/2²+1/2³+1/2⁴+...+1/2¹⁰)
va rog eu mult de tot dau coroana ce vreți voi​

Answer 1

Răspuns:

ex.23

Explicație pas cu pas:

a)

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

b)

$\frac{1}{2} - \Big(\frac{1}{{2}^{2}} + \frac{1}{{2}^{3}} + \frac{1}{{2}^{4}} + ... + \frac{1}{{2}^{10}}\Big) = \\ = \frac{1}{2} - \frac{1}{{2}^{2}} - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}}\\ = \Big(\frac{1}{2} - \frac{1}{{2}^{2}}\Big) - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{2}} - \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{3}} - \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} \\ = \frac{1}{{2}^{4}} - ... - \frac{1}{{2}^{10}} = ... = \bf \frac{1}{{2}^{10}}$