Question

помогите пожилусто все​

Answer 1

Ответ:

$\displaystyle a)S_{15}=32767;\\b)S_{15}=1047\frac{15}{16} ;\\v) S_{15}=10923;\\g)S_{15}=-1536\frac{3}{64}$

Объяснение:

$\displaystyle\boxed{\large a)}\\1) q=\frac{8}{4} =2;\\2) S_{15}=\frac{1*(2^{15}-1)}{2-1} =32768-1=32767\\\boxed{\large b) }\\1)q=\frac{256}{512} =\frac{1}{2} ;\\2)S_{15}=\frac{1024*\bigg(\bigg(\frac{1}{2}\bigg)^{15}-1\bigg) }{\frac{1}{2} -1} =\frac{1024*\bigg(\frac{1}{32768}-1\bigg) }{0,5-1} =\\=\frac{1024*\bigg(\frac{1}{32768} -\frac{32768}{32768}\bigg) }{-0,5} =\frac{1024*\bigg(-\frac{32767}{32768}\bigg) }{-0,5} =\\=\frac{-\frac{32767}{32} }{-\frac{1}{2} } =$

$\displaystyle =-\frac{32767}{32} *\bigg(-2\bigg)=\frac{32767}{16} =1047\frac{15}{16}\\\boxed{\large v)}\\1)q=-\frac{8}{4} =-2;\\2)S_{15}=\frac{1*((-2)^{15}-1)}{-2-1} =\frac{1*(-32768-1)}{-3} =\frac{-32769}{-3} =10923\\\boxed{\large g)}\\1)q=-\frac{512}{1024} =-\frac{1}{2} ;\\2) S_{15}=\frac{1024*\bigg(\bigg(-\frac{1}{2}\bigg)^{15}-1\bigg) }{-\frac{1}{2} -1} =\frac{1024*\bigg(-\frac{1}{32768}-1\bigg) }{-0,5-1} =$

$\displaystyle =\frac{1024*\bigg(-\frac{1}{32768} -\frac{32768}{32768}\bigg) }{-1,5} =\frac{1024*\bigg(-\frac{32769}{32768}\bigg) }{-1,5} =\\=\frac{-\frac{32769}{32} }{-1,5} =\frac{32769}{32} *\bigg(-1,5\bigg)=-\frac{49153,5}{32} =-\frac{491535}{320} =-1536\frac{3}{64}$

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справочные материалы:

$\displaystyle \bf q=\frac{b_{n+1}}{b_n} ;\\\bf S_n=\frac{b_1*(q^n-1)}{q-1} ,~~q\neq 1$