1-2-1-4-1-8-1-16-1-256-z-1-256-find-z-

Question Number 145499 by mathdanisur last updated on 05/Jul/21

\frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + \dots - \frac{1}{256} = \frac{z + 1}{256}

f i n d z = ?

Answered by gsk2684 last updated on 05/Jul/21

sum of 8 terms in G . P .

\frac{1}{2} (\frac{1 - {(- \frac{1}{2})}^{8}}{1 - (- \frac{1}{2})}) = \frac{84 + 1}{256}

Commented by mathdanisur last updated on 05/Jul/21

t h a n k s S e r c o o l

Answered by Ar Brandon last updated on 05/Jul/21

S = - \underset{n = 1}{\sum^{8}} {(- \frac{1}{2})}^{n} = - \frac{- \frac{1}{2} (1 - {(- \frac{1}{2})}^{8})}{1 - (- \frac{1}{2})}

= \frac{\frac{1}{2} (1 - \frac{1}{256})}{\frac{3}{2}} = \frac{1}{3} (\frac{255}{256}) = \frac{z + 1}{256}

\Rightarrow z = \frac{255}{3} - 1 = \frac{252}{3} = 84

Commented by mathdanisur last updated on 05/Jul/21

t h a n k s S e r c o o l