Question

Здравствуйте помогите пожалуйста

Answer 1

Ответ:

Объяснение:

1.

$b_1=500\ \ \ \ q=\frac{1}{5}\ \ \ \ S_5=?\\S_5=b_1*\fac{1-q^5}{1-q}=500*\frac{1-(\frac{1}{5})^5 }{1-\frac{1}{5} } =500*\frac{1-\frac{1}{3125} }{\frac{4}{5} } =500*\frac{\frac{3124}{3125} }{\frac{4}{5} } =500*\frac{3124}{4*625} =\\=\frac{4*125*3124}{4*125*5} =\frac{3124}{5}=624,8.$

2.

$-32;\ -16;\ ...\ \ \ \ S_{2-6}=?\\q=\frac{b_2}{b_1} =\frac{-16}{-32}=\frac{1}{2}.\\b_3=b_2*q=-16*\frac{1}{2}=-8.\\b_4=b_3*q=-8*\frac{1}{2}=-4.\\b_5=b_4*q=-4*\frac{1}{2}=-2.\\b_6=b_5*q=-2*\frac{1}{2}=-1.\\S_{2-6}=-16+(-8)+(-4)+(-2)+(-1)=-31.$

3.

$54;\ 36;\ ...\ \ \ \ S_6=?\\q=\frac{b_2}{b_1}=\frac{36}{54}=\frac{2}{3} .\\S_6=54*\frac{1-(\frac{2}{3})^6 }{1-\frac{2}{3} } =54*\frac{1-\frac{64}{729} }{\frac{1}{3} } =54*\frac{\frac{665}{729} }{\frac{1}{3} } =\frac{54*665}{243} =\frac{2*665}{9} =\frac{1330}{9}=147\frac{7}{9}.$

4.

$b_1=-4\ \ \ \ q=3\ \ \ \ S_{3-9}=?\\b_2=b_1q=-4*3=-12.\\S_9=-4*\frac{3^9-1}{3-1} =-4*\frac{19683-1}{2} =-2*19682=-39364.\\S_{3-9}=-39364-(-4+(-12))=-39364-(-4-12)=-39364+16=-39348.$

5.

$1;\ 3;\ 3^2;\ ... \ \ \ \ S_{2-5}=?\\q=\frac{b_2}{b_1}=\frac{3}{1}=3.\ \ \ \ \Rightarrow\\1;\ 3;\ 9;\ 27;\ 81.\\S_{2-5}=3+9+27+81=120.$

6.

$2;\ 2^2;\ 2^3;\ ... \ \ \ \ S_5=?\\q=\frac{2^2}{2}=\frac{4}{2}=2.\\S_5=2*\frac{2^5-1}{2-1}=2*\frac{32-1}{1} =2*31=62.$