Відповіді до завдань § 15 - § 21: 15.13

15.13. Знайдіть п’ять перших членів послідовності (c_n), яку задано

рекурентно:

1) с₁ = 8; с₂ = с₁ – 5 = 8 – 5 = 3; с₃ = 3 – 5 = –2;

с₄ = –2 – 5 = –7; с₅ = –7 – 5 = –12;

2) с₁ = –3; с₂ = 2 • с1 + 3 = 2 • (–3) + 3 = –6 + 3 = –3;

с₃ = 2 • (–3) + 3 = –6 + 3 = –3;

с₄ = 2 • (–3) + 3 = –3; с₅ = 2 • (–3) + 3 = –3;

3) c₁ = –2; с₂ = 3; с₃ = с₁ + с₂ = –2 + 3 = 1;

с₄ = с₂ + с₃ = 3 + 1 = 4; с₅ = с₃ + с₄ = 1 + 4 = 5;

4) c₁ = 0; c₂ = –5; c₃ = $\frac{c_2}{c_1+1}$ = $\frac{-5}{0+1}$ = –5; c₄ = $\frac{c_3}{c_2+1}$ = $\frac{-5}{-1+1}$ = $\frac{5}{4}$;

c₅ = $\frac{c_4}{c_3+1}$ = $\frac{5}{4(-5+1)}$ = $\frac{5}{-16}$ = –$\frac{5}{16}$.