Упр.18 ГДЗ Алимов 10-11 класс (Алгебра)

1) q= -1/2, b1 = 1/8;
2) q= 1/3, b5 = 1/81;
3) q= -1/3, b1 = 9;
4) q= -1/2, b4 = 1/8.

1. $$S=\frac{b_1}{1-q}=\frac{\frac18}{1-(-\frac12)}=\frac{\frac18}{\frac32}=\frac18\cdot\frac23=\frac1{12}.$$

2. $$b_5=b_1q^4,$$

   $$b_1=\frac{b_5}{q^4}=\frac{\frac1{81}}{(\frac13)^4}=\frac{\frac1{81}}{\frac1{81}}=1.$$

   Тогда

   $$S=\frac{b_1}{1-q}=\frac{1}{1-\frac13}=\frac{1}{\frac23}=\frac32.$$

3. $$S=\frac{b_1}{1-q}=\frac{9}{1-(-\frac13)}=\frac{9}{\frac43}=9\cdot\frac34=\frac{27}{4}.$$

4. $$b_4=b_1q^3,$$

   $$b_1=\frac{b_4}{q^3}=\frac{\frac18}{(-\frac12)^3}=\frac{\frac18}{-\frac18}=-1.$$

   Тогда

   $$S=\frac{b_1}{1-q}=\frac{-1}{1-(-\frac12)}=\frac{-1}{\frac32}=-\frac23.$$

Ответ

1) $$\frac1{12}$$; 2) $$\frac32$$; 3) $$\frac{27}{4}$$; 4) $$-\frac23$$.