Question

помогите решить 11 . 12 в 12  u=1/6

Answer 1

11.
$b_{1}=496* \frac{1}{2} =248$
$S_{6} = \frac{ b_{1}( q^{6} -1)}{q-1}$
$S_{6} = \frac{248 ( \frac{1}{64}-1) }{- \frac{1}{2} } = \frac{248*63*2}{64} =488, 25$
12.
$\frac{ q^{2}-4 v^{2} }{4vq} * \frac{2}{q-2v} = \frac{q+2v}{2qv}$
$\frac{ \frac{1}{5}+2* \frac{1}{ 6} }{ 2*\frac{1}{5}* \frac{1}{6} } = \frac{ \frac{1}{5} + \frac{1}{3} }{ \frac{1}{15} }$
=$\frac{8*15}{15*1} =8$

Answer 2

$b_{n}=496*( \frac{1}{2}) ^{n}\\\\ b_{1}=496* \frac{1}{2} =248\\\\ b_{6} =496*( \frac{1}{2}) ^{6} =496* \frac{1}{64} =7,75\\\\S _{6} = \frac{ b_{6}*q- b_{1} }{q-1}\\\\ b_{6}= b_{1}* q^{5}\\\\ q^{5}= \frac{ b_{6} }{ b_{1} }= \frac{7,75}{248}=0,03125\\\\q= \sqrt[5]{0,03125} =$$=0,5 S_{6}= \frac{7,75*0,5-248}{0,5-1}= \frac{3,875-248}{-0,5}=$$= \frac{-244,125}{-0,5} =488,25\\\\\\( \frac{q}{4v}- \frac{v}{q} )* \frac{2}{q-2v}=$$= \frac{ q^{2} -4 v^{2} }{4qv} * \frac{2}{q-2v} = \frac{(q-2v)(q+2v)}{2qv}* \frac{1}{q-2v} = \frac{q+2v}{2qv} = \frac{ \frac{1}{5}+2* \frac{1}{6} }{2* \frac{1}{5}* \frac{1}{6} }= \frac{ \frac{1}{5}+ \frac{1}{3} }{ \frac{1}{15} }= \frac{ \frac{8}{15} }{ \frac{1}{15}} =$$=8$