Відповіді до завдань § 15 - § 21: 20.6

20.6. Знайдіть суму шести перших членів геометричної прогресії:

1) b₁ = 1,5, q = 24 : 6 = 4. S₆ = $\frac{\mathrm{1,5}(4^6-1)}{4-1}$ = $\frac{\mathrm{1,5}(4026-1)}{3}$ = 2012,5;

2) b₁ = –4, q = –$\frac{1}{2}$. S₆ = $\frac{-4•\left(\right(-\frac{1}{2}{)}^6-1)}{-\frac{1}{2}-1}$ = $\frac{-\frac{1}{16}+4}{-1\frac{1}{2}}$ = $\frac{3\frac{15}{16}}{-1\frac{1}{2}}$ = –2,625;

3) b₁ = 2, q = 2. S₆ = $\frac{2(2^6-1)}{2-1}$ = 2⁷ – 2 = 126;

4) b₁ = 2, q = $\frac{1}{\sqrt{2}}$. S₆ = $\frac{2•\left(\right(\frac{1}{\sqrt{2}}{)}^6-1)}{\frac{1}{\sqrt{2}}-1}$ = $\frac{2•(\frac{1}{8}-1)}{1-\sqrt{2}}$ • $\sqrt{2}$ = $\frac{\mathrm{1,75}\sqrt{2}•(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}$ = $\frac{\mathrm{1,75}\sqrt{2}+\mathrm{1,75}•2}{1-2}$ = –1,75$\sqrt{2}$ – 3,5.